Okay that's a little weird because I've got the 14 Panzer and 29 Motorised (PzGr) caught up in the suburb of Yelshanka and the area around the southern train station in October. Certainly not somewhere safely in reserve. In November the 14 Panzer switched to come around at the northern suburbs and pressed at the Barrikady factory along the river bank, forcing Soviet defenders further into the city. But it suffered great attrition during these manoeuvres. It wasn't large tank forces they faced, one tank corps only managed to get about a dozen KV-1, 40 T-34 and about 30 T-70 across the river but the fifty combat worthy tanks were tough as hell, and the little T-70's turned out to be supreme urban-battlewagons, using rubble concealment, a very heavy 45mm gun for their class and their tremendous mobility. Panzers found they could be outmatched in the open and get caught in trouble within the city rubble, the PzIV in particular has its armour concentrated towards the front and is very poorly suited to urban warfare. And we're not even talking about Soviet artillery yet.
On the northwest flank the Soviets held 150km of bridgehead between Kletskaya and Serafimovich from September onwards. The only rearguard allowed to support the Rumanian flank was the two infantry divisions, yes count 'em of VIII Armee K which was all Hitler would allow. Paulus had XI K in addition covering his headquaters, which is effectively the reason they happened to be in the Don Bend region but not as a reserve, they were what Von Weichs hoped was a front, but as they were attached to the 6th Armee it had to be considered a broken front. If Paulus HQ moved, so would they.
This lack of reinforcement was due to Hitler's explicit orders that the XXIV Panzer K was not to leave any rearguard of its armoured formations to protect the flanks maintain a continuous front (one General was sacked for this), which would've turned XI K into a reserve for Paulus. Hitler designated Luftwaffe infantry to support the Rumanians instead, but then in November he cancelled their actual attachment to Rumanian formations due to their inexperience in field operations.
The only arguable reserve you appear to have referenced is the 22 Panzer which had 50 serviceable tanks, the only forces left to hold the Don Bend and these were on standby to counter the expected attack at Kletskaya, but then was redirected to Serafimovich further west. They supposedly reinforced the Rumanian V Armoured Corps (what little of it actually had armour) but what in fact happened was both of them ran headlong into the Soviet 5th Tank Army (something like 500 AFVs) and got pretty much annihilated. Ceased to exist. Whatever was left of the Rumanians on the Don Bend got encircled by three armies and fought to breakout south. For a bit of amusement the Soviet tanks were flanked by two corps of horse riding cavalry, which actually proved exceedingly competent at mopping up entrenched positions after the tanks had rolled past taking out any hardpoints.
And the awkward thing here was acting-Generalfeldmarschall Heersgruppe B von Weichs was giving them one set of orders by radio, and Hitler was sending different orders to them by courier. Go here, no go there, retreat, no don't retreat attack, wait retreat again, no wait go rescue the Rumanians.
Another point, one should recall the manner of replenishment in Stalingrad. The Panzer formations took StuGs from the Motorised formations to replace Panzers and Marders from the Panzerjäger to replace SPG's, the Panzergrenadiers took armoured cars from the scout formations to replace their StuGs and the Panzerjäger took field guns from the Infantry to replace their Marders. When someone asked for reinforcements, if it was absolutely necessary, since no reserves were available Paulus just reassigned battalions as brigade attachments, continuously cannibalising and weakening his formations. Hoth's 4th Panzerarmee (which was really a corps) went from almost no tanks and an infantry division upon arrival to combat worthy again in this fashion for example, back in September. But what it did mean was half his formations were now Czech light tanks and Rad8 armoured cars instead of battle ccompetent Panzers, at least until they were slowly replaced from German rail supply as available (with the latest PzIIIJ, IVG and StuGIIIF which was nice), but it was a much slower process. Hence the Pz div requisitioned StuGs and Marders from the PzGr, etc. And it sapped divisions from elsewhere on the front. The Don Bend was regarded by OKH (clearly stated) as a broken front, which was the cause of severe arguments between Zeitzler and Hitler (who probably wondered why he bothered sacking Halder).
True that during Uranus, at Kletskaya once 22 Panzer struck west the 14 Panzer withdrew from Stalingrad and raced upstream of Kalach, where the German bridgeheads for the 6th Armee had originally been made from the Don Bend. These were the target of the Soviet 65th Army driving southeast as it would cut off the German rear and isolate everything committed to Stalingrad for encirclement. But they were slowed by the XI Armee K rearguard (not particularly well equipped) and the terrain. The 14 Panzer got back across the Don and started furiously counterattacking them before they could press the advantage. What little of 14 Panzer had even managed this famous feat did little more than slow the advance however. In fact the entire XXIV Panzer K including the 3 and 60 Motorised and 16 Panzer had been ordered from the Stalingrad suburbs along with 14 Panzer (which had been variously attached to LI Armee K or 4th Panzerarmee), but they didn't have the fuel or ammunition for it.
By this stage in the South Hoth only had two German divisions left again himself, though he requisitioned the Rumanian 4th Army as attachments. They had no armour or useful antitank capabilities though and were quickly routed in action after losing three divisions to the last when three Soviet armies attacked and broke through. Hoth did pull elements of the 29 Motorised out of the city (which was also variously attached to LI Korps or Hoth) and held it in reserve on the eve of attack, but they got slaughtered when the Rumanians routed and they'd tried to take up the slack.
What wound up happening is five days of brutal attrition and a Soviet linkup at those bridgeheads near Kalach I was talking about. By the end of December Von Weich's described the forces available to Manstein with which to regain the situation as "no more than a strategic expression." The 4th Panzerarmee for example on the 24th November consisted of about three Rumanian infantry and one cavalry division, who had routed quickly enough to escape the slaughter (ordered out to billet on the Kalmuk Steppe Hitler was so upset with them, but alas could not order them all shot because they were all that was left of Gruppe Hoth).
I don't know mate, I'm just not feeling you on the already having reserves thing.
Once again I think that a fully maintained 17th Armee sitting comfortably at Nizne-Chir and reinforcing the Don Bend, well for a start there was always the issue of that 150km bridgehead on the northwest flank. That's what did it. The Soviets sat there for three months happily amassing three armies, a thousand of the latest tanks, 13500 artillery pieces and a million infantry, not including SPG's or katyushkas, right smack bang in full view of Luftwaffe reconnaissance photographs and fly overs. It wasn't any secret. It was simply something there were no reserves to deal with back when it counted.
You know and the 4th Panzerarmee was only ever at corps strength, combine von Kleist and Hoth and you've got one tank army. That's what should've been the southern flank.
Still a horrific battle, but at least an even chance.
As for what to use in the original concept Von Weichs had in mind of sitting back and blasting Stalingrad to oblivion, heavy artillery. Bombers. The fact that the solid and continuous, strongly held Front is now the river Don, 50km west. It would've reversed the situation, with the Werhmacht in a natural fortress and the Soviets needing to extend for attacks, with vulnerable flanks. Otherwise they could just sit there for the next year and blast and bomb away at the place, why ever get closer than about 15km? The place isn't going to be much good as an industrial and transportation centre under those conditions and you can look at tightening the Front up elsewhere on the continent. Bomb Grozny, Maikop and Astrakhan out of existence. Keep it simple, just stop the Soviets from using much, not try to take it all. Plus the bonus is holding the Don and cutting across the Kuban means no US lend lease shipments through the Middle East, they can only use the Siberian railway and that wasn't even fully operational until 1943 after the Americans sent them, well trains, train tracks, engineers, a partridge in a pear tree.