I suspect that your numbers are airframes not completed aircraft ready to be accepted by the Luftwaffe:Production numbers prior to June 1944 was about 60 per month. In fact it was 60 units in May. The units did not begin combat operations until June 44 though. 29 units Approx. matches the Jabos reported placed into operations to Hitler in July, and not the total number available.
"The next month, June 1943, Messerschmitt himself was called before the RLM to report on the status of the proposed production of the Me262. While it was still in testing, he predicted that his company could not commence delivery of operational Me262s before January 1944. Messerschmitt was optimistic about the Me 262 program but he was realistic about his companies manufacturing capabilities. He predicted that his company could start production in January 1944 and be able to deliver by the end of each month 8 in February, 21 in March, 40 in April, and 60 in May. There after he promised 60 aircraft each month through November 1944. At this point he noted that these were only airframes! He specifically pointed to the fact that he was in control of pruducing the aircraft, the Junkers engines were another matter altogether. [...]"
"When Beauvis did finally fly the jet in October the RLM again expanded it's order to thirty 0-series aircraft [ie pre-production models], with the stipulation that they would be completed by the end of 1943. However Messerschmitt rejected the order on account of his lack of production capabilities; he promised only 10 airframes by the deadline."
Quoted from The Jet Race and the Second World War
Neither was reliable. The early Jumo 004s that powered the early prototypes were hand build 004A prototypes, NOT pre-production models and were never intended for mass production - being far too expensive both in man hours and strategic materials. The delays caused by redesigning the engine for mass production - the 004B were protracted and at first cut running time from the 100+ hours of the A model to less than 10.I think this is the BMW engine, not the Jumo engine that was unavailable as a reliable unit until late war.
Galland and Milch may have been enthused about placing the Me262 into immediate mass production but Director Cambeis, the Junker's representative of the Me262 overseeing commission was totally opposed to it.
Eventually after dealing with problems with the compressor blades reliability was up to 25* hours and the design was frozen for mass production, despite continued Junker's engineer objections, in June 1944.
*the 25 hour longevity was measured on the test bench, NOT operational conditions. In actual operating units only the bomber units remotely came close to that time. In part because they began their conversion earlier and their mechanics were more experience but mostly because their missions didn't require sudden throttle actions that drastically shortened the life of the engines.
"Developing the new power unit was difficult enough, but German engineers faced a further problem. Owing to the Allied blockade; the hardening elements necessary for effective high-temperature-resistant steel alloys-in particular, chromium and nickel-were in short supply. Only limited quantities could be spared for the jet-engine program, so those who worked on the new propulsion system had to make the best of what was available. For the Jumo 004 engine that powered the Me 262, Junkers engineers used some substitute materials that were not up to the job.
For example, the combustion chambers were made of mild steel and coated with baked-on aluminum to prevent them from oxidizing. When the engine was running, these combustion chambers slowly buckled out of shape. The turbine blades were made of a steel-based alloy that contained some nickel and chromium. That material was insufficiently resilient, however, when the engine was running, the centrifugal forces used the blades to elongate, or "creep."
Limited by combustion chamber buckling and turbine blade"creep," the running life of pre production Jumo 004s rarely reached 10 hours. Throughout a flight, careful throttle handling was vital to avoid having an engine flame-out or overheat. At altitudes of above 13,000 feet, the engine became increasingly temperamental, and if it suffered a flameout, the pilot had to descend below that altitude before he attempted a relight. In its early form, the Jumo 004 had too many weaknesses to allow mass-production.
After much hard work to improve matters, late in June 1944, the Jumo 004B-4 emerged with a running life of 25 hours. That still wasn't impressive, and certain reliability problems remained, but the Luftwaffe couldn't afford to wait any longer. The design of the Jumo 0048-4 was "frozen" and the unit was put into mass production. During Sept '44, Jumo 004B-4 production reached significant levels, and that month, the Luftwaffe took delivery of 90 Me 262s"
While it's true the Jumo 004 was being disperssed among many different projects, most never made it past prototype stage. The only real competitor for the Jumo 004 engines were the Arado 234. The first AR234 pre-production model did not appear until May 1944, and the type didn't become operational until Sept 1944 - total production till the end of the war only 210.The Jumo engine was available, however, in numbers prior to June 44, but the problem was that it was dispersed among several other projects, which held down delivers of the 262. This was once again down to Hitler. For example, Hitler had dreamed up the idea of the Salamander jet that would be flown by Hitler Youth pilots. This was a total waste of resources. The Salamader was actually more demanding of pilot skill than was the 262.
The He 162 wasn't conceived until September 1944 and was largely the brainchild of of Speer and party leader Otto Saur. It was to be powered by the BMW 003, instead of the Jumo. While undoubtably a waste of resources it in no way impacted the operational availability of the Me262 in 1944.