I enjoy the technical side of these discussions because I seem to learn quite a lot from those experienced in varying fields. I nodded along with the theory that the Foxbat's antenna should be vertical and even agreed with the reasoning but then realised that I fly with a very similar aerial set up to the OP's and do not have the problems he has. Yesterday I experimented with all sorts of directions for transmitting and receiving and nobody noticed any difference.
I considered that my antenna may be actually more horizontal than the OPs but I don't actually think this is the case. When I'm in the flying attitude I reckon the long bit of the antenna points up at about the same angle as the Foxbat's.
This is in an RV4 (so it's metal, as per the Foxbat) and the antenna looks very similar. Also, coincidentally, the transponder aerial looks to be in a similar location to the Foxbat's and I have no problems on that score either.
I am not going to argue that making his antenna vertical will not solve the problem but my experience, albeit in a different aircraft, is that there may be other gremlins afoot.