Although the BRM's big problems can be fixed by installing a BEW cam, I thought.
Mechanically, at least the bottom end of any EA113 engine - for US-spec TDIs, that means ALH, BEW, BRM, CBEA, CJAA, and CKRA - should bolt in with no modifications into any Mk4 or newer car. (And, EA113 engines can also bolt into Mk2 and Mk3 cars after tapping the rear mount holes.)
I believe the Mk5/6 transmission mounting is slightly different from the Mk4, so you'd need to use a Mk5/6 transmission, but that shouldn't be a problem - anything that you'd want that's manual and TDI-compatible is available, between the BRM's transmission, and the various CBEA/CJAA/CKRA transmissions.
I believe, however, that you may run into trouble with clearance for the turbo, in a Mk5 or Mk6 car - the BRM has the turbo in a different place, IIRC. However, a BRM or other Mk5 8v TDI turbo setup should, in theory, bolt onto an ALH or BEW head.
In any case, the electrical hurdles of integrating ALH engine management into a Mk5 or Mk6 environment may make this incredibly impractical. Even with a CAN-capable ECU, quite a few functions won't work any more, or won't integrate properly - including such things as the power steering.
A BRM may integrate better, because its ECU is already designed for the Mk5/6 electrical environment, although there may still be a few missing functions.