I had this conversation with a mx fed years ago. What he shared was that the only thing required to actually be TSO'd was a GPS to be used for terminal operations. If you as the builder say the equipment works as planned, and test / prove it in your phase one testing, there you go. That's why we have phase one, and after a mod like that the feds would want you to do another phase one period.
Something this fed added was that there were at least some Pipers built with non-certified instruments and that the plane as a whole, with those instruments installed, was certified. Very interesting stuff, and not something I'd have ever guessed.
Certainly the rules could have changed in the intervening time, so were I doing this I'd place a call to OSH and ask the guys that interface with the DC feds regularly and get their take on the current paradigm.