If my plane had nothing but GPS-based avionics, what would my
options be?

Vectors.

Ray Andraka wrote:
Doesn't leave you any out should comm go down. I've had that
happen due to P-static, ice on the antenna, and problems with the
radio in a rental.

Now you're theorizing about a simultaneous double system failure -- GPS
and communications. It's impossible, just extremely unlikely.

You can keep adding redundency to get the probability of incapacitation
as low as you want, but eventually an event will happen which will take
out all of your backups at the same time. What's the odds of a DC-10
having all three hydraulic system fail at the same time? They said it
was impossible, yet it happened (Souix City, uncontained failure of a
turbine disk).

By far the most likely cause of simultaneous GPS and COMM failure is
loss of ship's electrical power. It would take out your VOR, ILS,
Loran, too. The way to protect against that is multiple electrical
busses (like in twins), or battery backup and/or handheld devices.