RE: What could cause this?
I believe your problem is using a 6 volt battery pack. Futaba radios do not seem to like the higher voltage. A friend of mine was experiencing tail surface glitching on his F-104 which always occurred when the plane was turned on for the first time after a fresh charge. He uses 4.8 volt packs but after a fresh charge, these batteries will produce well over 5 volts for a period of time. His glitching always went away after the receiver was on for a few minutes and the voltage dropped down some. He was using a Futaba 8UAP PCM radio. PCM radios won't show the glitching from interference (i.e. from loss of signal), they just go into failsafe mode. So, I can conclude that his glitching was not from any external source since his radio never went into failsafe.
I think your problem will go away if you convert to a 4.8 volt battery pack. If you are concerned about current drain from the digital servos, I suggest a higher mah rating on your onboard pack like the 3000mah packs I use in my jets.
If you don't think this is right, I suggest you post your question in the Futaba Radio Support subforum and see what they have to say about it.