using stolen goods for a mitzvah - mitzvah haba'ah b'aveira (II)

Returning to the machlokes Rabeinu Tam and R"I whether a thief who now owns stolen goods because the original owner had yeiush can use them for a mitzvah, the simplest explanation of the debate is whether the problem of mitzvah haba'ah b'aveira is dependent on dinei mamomos kinyanim or is an issur v'heter issue that disqualifies the object because of its having been stolen irrespective of the thief's current dinei mamonos status as owner. In the Reshimos Shiurim (collected from the Shiurim of R' Soloveitchik) on Sukkah 30 an additional interesting hesber is offered. Rabeinu Tam as quoted in the Sefer haYashar seems to limit the disqualification of mitzvah haba'ah b'aveira specifically to lulav and korban. If mitzvah haba'ah b'aveira is a psul in the mitzvah object, why is this disqualification limited to just these two cases? The Rav therefore suggested that mitzvah haba'ah b'aveira here is not a psul in the cheftza shel mitzvah, the object per se, but a psul in the criteria of 'lachem', ownership, which the mitzvos of korban and esrog specifically mandate. Even if a thief has kinyanei gezeilah and now owns the stolen goods, this level of ownership attained via crime is insufficient to meet the criteria of lachem which the Torah demands. Based on this approach, one can also answer Tosfos’ question (Sukkah 9) on why a separate pasuk of ‘lecha’ is needed to disqualify a stolen sukkah and the rule of mitzvah haba’ah b’aveira is insufficient (see Daf Notes here). Without the extra pasuk, yeiush and other kinyanim which transfer ownership to the thief would allow him to use a stolen sukkah; however, based on the criteria of ‘lecha’, similar to lulav and korban, such a sukkah would be disqualified.