The short range of the "E" was solved in two ways. One was the drop tank, Just a few weeks or months late late to make a big difference. Two was the change to the "F" series fighter, the cleaned up nose, modified radiators, elimination of tailplane struts and other details offered a reduction in drag which not only increased both speed and climb but range as well, fast speed at same power level=more range.
You are right. There was also issue of engine better fuel consumption. 601E better than 601. Less consumption. This plus less drag = 20% more range for 109F. Equal conditions. Droptank added bonus.
The range issue starts creeping back in with the "G"s. More weight doesn't mean that much more drag at a given speed but it does mean more fuel burn in a climb to given altitude. As lumps and bumps start to appear on the aircraft drag starts to increase. While the "G" may be able to cruise at very similar power settings to an "F" using the extra power of the 605 engine over the 601 will increase full consumption for the minutes the extra power is used. Any power boosting system (MW-50/GM1) will also significantly increase fuel consumption for the few minutes it is used. The more powerful 605 engines used in the later "G"s used fuel at an even higher rate in combat. With an essentially "fixed" fuel supply something has to give and it's range. The difference between the normal take-off rating (1475Hp?) of the 605AM and it's emergency rating of 1800-2000hp for 5 minutes is the same amount of fuel as it needs for 9-10 minutes of economical cruising flight.
Theory is correct, but you much overstate.
In practice, 109G range same as 109F. Reason again is 605A is better fuel factor than 601E. Keep reasoning that compression ratio of engines increased.
For example. 605A max. power until almost 1944 - 1310 HP. Fuel consupation - 400 liter. For 601E - 1350 HP, for 445 liter. This is 1942-43. 1944. 605A, 1475 HP - 480 liter. With 605AM, 1800 HP, 560 liter.
This is paper form.
Thanks to Juha, we know Finn measured in practice better consumption. This is probably to safety tolerance by manufacturer - statng higher consumption in manual, just in case.
Example needs to as five minutes you say, maximum power allowed, ie. combat. 601E vs..
605A 1942/43 -40 liter consumption per hour for 5/60: + 3,3 liter in tank. So actually G model is better using fuel in combat..
605A 1943/44 +35 liter consumption per hour for 5/60: - 2,9 liter in tank.
605AM 1944 +115 liter consumption per hour for 5/60: - 9,6 liter in tank.
See worst case, 605AM engine. How less range can be due to WEP use? We assume worst condtion for 109G. Meaning, how less range will be, how much less 9,6 liter fuel makes difference in range if best range condition would be used? I will assume same cruising speed/consumption as 601E/109F: 130 liter/410 km/h Note 605A is consuming fuel better probably. 9,6 liter is 7,4% of 130 liter. This is how less time can be spent at best cruise. Ie. 7,4% less time - 4,5 mins less - at 410 km/h cruise allowed - 30 km covered.
Meaning. Difference between 109F range and 109G-14 range (605AM) due to "The more powerful 605 engines used in the later "G"s used fuel at an even higher rate in combat. " -
only 30 km..!!
Very insignificant IMHO. Difference in serial manufacturing will mean more.. this is within scatter error. On other hand, its quite possible that overall better consumption of 605A in cruise more than makes up for this. Germans considered 109G longer ranged than 109F. Power boosting system on overall fuel consumption, range - insignificant. You overstate this in analysis.
Also, increase tankage on 109 is possible. It was done. 109B to 109C. 109C to 109E. 109G to 109K. Very easy. I am thinking you are wrong in conclusion it was done in Spitfire because it was more room, in 109 no room. On Spitfire it is more difficult - tanks are sandwhiched between cocpit and engine, not possible to increase their size, only if another tank is placed elsewhere. In 109, tank is in rear fuselage, there is space until tail.

It is fact that it was increased. Also in general you may overstate difficulty. For example, Jakovlev 9 series. Range was really short in base variant. But
when people wanted - easy to increase. 9D and 9DD variants - very long range. Extra fuel was added.
It is no black magic.
Here's error - Spitfire range went down with later variant, always. So need to increase tankage to keep range. 109 - range always went up. Range went up from 109E to 109F. Same tankage. Range went up from 109F to 109G. Same tankage. 109K - only limited information. Rare plane at war end, much destroyed. But datasheet suggest range went up again, too, in high speed cruising conditions. Same as 109F - cleaner airframe, better engine - higher ratio of compression always increasing. 601A - 6.9. 605A - 7.5. 605D - 8.5. Better effiency. Adding fuel tankage - possible. But why add more fuel, is there need when with same fuel tank and better engines, range actually goes up..? It is not question of lack of possibility, but lack of will. What technical reason do you think exist increasing fuel by say + 25 %? I am cheating - this was done.. MW tank could hold +115 liter.. you say it is impossible, but it was done. General tank can be increased too. I do not see reason why cannot make it bigger, to hold more fuel. Space is there. Weight is there. They considered making K-6 some 500 kg heavier than, do not tell me impossible.. or give good reason why you think why.
We can put big MYTH stamp on it. 109 had no range issues - after 109E of course. Actually, 109E is shortest ranged variant. Lower than Jumo powered versions. Lower than later versions. Unfortunate for Germans this happened variant present when they critically needed range - BOB. But afterwards - range is good, almost triple 109E. Same as Fw 190. Less than Ta 152 of course.