Not a 56TC pilot, but the Dukes have the same engine. 45-50 gph fuel burn for the 380hp output, the Baron must be a rocketship to fly. But, support for the TSIO-541 engines is dwindling, you can't get a new one from Lycoming, though they do still make new cylinders. Parts get harder and harder to find, yes, you can still get what you need, but it seems like everything needed requires a "where's waldo" treasure hunt to discover parts sources. You can still get overhauls done, but only a handful of shops across the country do the -541. Cost for the overhaul, engine with engine accessories like turbo, fuel pump, etc., but not alternator, prop governor and so forth, is on the order of $65K per side. Still want to play?
As great as the 56TC may be to fly, it's just too rare, heading towards the museum/antique realm. Personally, if I needed turbocharging capability, I'd look at the 58 Barons. But, as others suggest, IMHO, the 55's, Travel Airs, or, even a Seneca, would be a much more viable choice for twin time-building.