I tried to get Thompson Center interested in making a syn stocked double in 405 Win and 375JDJ but they didn't even reply.

Those would be my picks. With a set of 20 or 28 ga bbls to go with it.

Short of that, buy a FinnClassic 512S in 9.3 with a set of 12 ga bbls and get rid of everything else except your 22lr (or maybe your varmint rig) and your super heavy DG double.