I remember hearing a story some time ago about how the UK tied up Turkish chromium production in advance contracts pre-war so Germany would have serious problems with this.
Tungsten similarly was another much needed material they had problems with.
If you upgraded it, you'd have to come up with the space somehow. If you move the engine forward, then you'd have to move the wings for CG purposes or, alternately, extend the rear fuselage for CG purposes. If you did that, what other effects would be generated?.
Compared to BMW 801D (i.e. most common version)
1,010kg.
2,006mm long. 1,290mm diameter.
Additional length and weight shouldn't be any more an issue then with Fw-190D9. Rear fuselage plug will still be necessary.
Not sure about 150mm additional diameter.
It was proven in the 190D and Ta 152 aerodynamically, but they never fielded turbo Fw 190 in combat as fas as I know. Mu conclusion is that either the turbo wasn't ready or the developmental issues were so many it was shelved.
Of course, there might well have been other reasons than these two. Perhaps every time they got a turbo plane together it was destroyed by bombs before flying enough to accumulate data. Whatever, it didn't make production.
As Gixx said - they added fuselage 'plug' to cater for CoG once the Jumo-213A was added. Plus, when the Ta-152 was engineered, Fw further made more space between engine and firewall, so more ammo boxes can be installed (five total!), along with a MK-108. The wings were also relocated further in front.
The complete power pack - turbo, inter-coolers, engine itself, cooling fan, plus the table with specifications (from AEHS):
If Germany had wanted to mass produce turbocharged BMW801J engine when would it be ready? Presumably not before 1943 as it took about that long to sort out BMW801D engine.
'Wanting' was not equal to having a capability. It took a while for the Germans to come with a way to 'fight' the hot exhaust gasses via hollow turbine blades. At any rate, for the turbo 801 to have an effect to ww2, it must be available in good numbers by late 1943 IMO.