I don't have issues flying through precip either, but I have a metal plane. Ask around on the various forums for the types of composite aircraft you are interested in. In addition to static problems messing with the radios, the parts inside that ARE metal can develop pretty nasty charges on them when flying through static-inducing situations. You don't need to be in a cell to experience this.
The RV's are not bad platforms for this and are certainly ubiquitous. Here's a story from one such composite flyer that...
I recently flew my Glasair from LA to Boston and back, in the process
picking up 14 hours of actual. (I had about 700 hours at that time, with
about 100 hours TIT.) I have one comment: If you are going to fly IFR in
a composite airplane, do not fly anywhere near a thunderstorm. A level 3
cell does not mean be cautious in a glass airplane, it means find a hotel.
I picked up some static electricity over Cleveland that was extremely
severe and quite painful. Since the fuselage is not conductive, the charge
flows where ever it can, with a preference for sharp points and edges....
in my case every switch on the panel as well as the prop and throttle cables.
All the avionics went out, and the charge actually started arcing across the
cabin. Note that I while I was in the clouds, I was not even very close to
the actual cell. It was no fun being blind and deaf in the soup and getting
shocked every time I touched anything. (I got the radios back after a few
minutes and was able to land safely.) Icing however, is not a real problem
at all, as long as you stay away from anywhere known to be severe. I flew
right through an are where the 4 planes ahead of me had reported rime without
even a trace. It takes alot to ice up a composite airframe.