Can the GT2 be retrofitted with the GTS transmission?

I'm looking to get an AWD GT2 in the next few months, probably after the 2021 facelift. The only thing I feel is missing from the GT2 is a mechanical LSD.

Is it possible to install the rear differential from the RWD Stinger or GTS in an AWD GT2?

Another nice to have (but would probably never be used except to wear out some tires) is the D-AWD mode which puts all power to the rear wheels. Is this just a TCU program, or are there mechanical differences? If it's just a transmission control program, can it be flashed to the GT2?