I remember that popping up in a book about the He 177. I'm surprised that would have been a problem despite having poor oil resources, they did start using synthetic POL as early as 36.
Plus they were producing so many different aircraft designs and didn't seem to have a central clearinghouse to weed out designs that couldn't hack it.
There was certainly a serious oil problem, having to supply not only themselves but occupied Europe and Axis allies with fuel, however they had enough to run a small fleet of 4 engine aircraft. The fuel shortage became acute in the lead up to operation overlord when allied bombers began targeting the German oil industry around March/April/May to cause maximum shortages prior to the invasion. They had in fact avoided targeting the German oil industry so that it didn't have time to take measures. After the oil industry campaign and D-day created severe shortages there was no point keeping any bombers and they were mostly scrapped.
Note also that one objective of the German Army was to capture the Caucasian Oil fields. Had they been captured, put into production and held German oil problems would be over. The German high command (under Halder) and Hitler were at odds. Hitler wanted to conduct a campaign to capture materials, Halder though that capturing Moscow would cause a political collapse.
The Germans had planned to produce 100 heavy bomber aircraft per month from when the latter batch of He 177A3 received DB610 engine (paired DB605) replacing the DB606(paired DB601). The He 177A5 with the engines was achieving 220 hours MTBO by later 1943. 100/month is 1200 Year is perhaps 5%-10% of allied production. They would have been very useful in reconnaissance, special missions especially with the various guided weapons they were continuously improving. The He 177A5 had the lowest attrition rate of any Luftwaffe aircraft during the baby blitz.
After the oil industry campaign and severe shortages there was no point keeping any bombers and they were mostly scrapped. Bombers for the 1945 Luftwaffe was Ju 388 or Do 335 with maybe the Ju 488 (service ceiling over 48500ft with the BMW801TJ, probably more with the BMW801TQ and jet aircraft. A few piston designs were kept for special missions (long range or ultra high altitude)
The Plans for the He 177 were the He 177A7 which incorporated the improvements such as powered tail turrets with much more powerful DB613 engines (paired DB603) however by this time everyone wanted to move away from paired engines as fast as possible so the wing for the He 177A7 was engineered to be able to take 4 separate engines which is the He 277 Similar to what Airbus did with the A330/A340.
I dont think the Germans were producing too many prototypes, they were producing too few. The allies were able to produce a myriad of prototytpes.
The backups to the Ju 288 nor He 177 never got past a single prototype whereas the UK produced Manchester, Lancaster, Sterling, Warwich. The US had B17 B24, B29, B32 etc.