Owners have not done this because in order to prove that a non-TSO'd piece of equipment meets the requirements of a TSO, you'd have to go through the whole range of TSO testing. In which case, if you passed, just get the damn TSO. Since no experimental EFIS/GPS manufacturers (Dynon, Garmin, etc.) has done this, there must be a good reason - it's hard and a lot of work, and their equipment does NOT meet the TSO requirements (RAIM, etc.).
It's NOT legal to use non-TSO'd or non-TSO'd equivalent equipment for IFR, and no-one will tell you that a non-TSO'd piece of equipment meets the requirements of the TSO.
No can do. Either install a TSO'd navigator (GPS-175, GNS-650, Avidyne IFD-440, etc.) or don't shoot GPS approaches or use GPS as the primary navigational means enroute.
Now, since it's legal to use a ham sandwich as the primary means of IFR en-route navigation (i.e., pilotage, dead reckoning, etc.) as long as you file your route assuming that primary means, you can use any GPS (or anything else) as your SECONDARY means of navigation. But this only applies en-route.