I know, it's just that the one in the 1,400 million year orbit wouldn't stay in there for very long. The one that is 6.5k AU out is fine since the Oort cloud lies even further out.
Anyways, it looks like its a case of you having the planet so far out. Also, given that you have a neptune mass planet close in, I observed the wobble and it's in tune (more or less, there was some buffering from the other planets) with that planets orbit. So what you are seeing is in fact, an effect of the stars wobble, plus the very long orbit period seems to magnify the effect. Not sure why a bigger inclination dampens it though, unless you maybe had it set on zero inclination.