I am not familiar with the GTNs but I believe that, like the GNSx30 boxes, they can be installed as "simple" (non ARINC) boxes so should interface to existing avionics conventionally.
Yes of course it is a lot of rewiring, with the usual cans of worms possible, and no responsible avionics shop should suggest otherwise. I wouldn't do it at this time of the year. Wait till the winter
If you want to fix the radio then put in a KX155A, or KX165A if you want 8.33 (not much point on a TB20 whose ceiling is only just FL200, though I have one). You can get these radios, overhauled, from the USA e.g. South East Aerospace. May have an issue with an 8130-3 on used kit, unless you process it via a Part F company into an EASA-1 form.