I think what you are suggesting is possible (in theory anyway) but FAR from simple.. I did explore a similar group of ideas for my FrAEdom range of "Theremins" - but, as people here have no doubt realised, when I have thought of something and done a few 'proof of concept' tests, I have a tendancy to think the job is nearly done - I am starting to learn that, with theremins, the job aint done till the lady sings!
Problems: GRAVITY - can be solved by a neck strap.
BODY CAPACITANCE: - You will need to ensure that there is either a constant capacitance between your body and the instrument, so that only your hands / arms influence the fields, or that you have a capacitance "invisibility screen" between your body and the instrument.. I think I am the only person with access to "invisibility screen" technology at present! ;)
Forget protruding antennas - use insulated metal plates on the guitar body, Art Harrison has some designs you may be able to adapt.
You need a Theremin 'mute' switch, then you could mix the guitar and theremin outputs when playing theremin.. This could giva an advantage as the strings / pickups would still be free to get feedback from the amplifier .. could (combined with the severe difficulty you would have getting any kind of tunefull playing from the instrument) lead to soundscapes of unimaginable complexity !! 8(