Steven, There are a ton of folks on this site more experienced than I, but I have been doing this a while myself.
I myself would consider a few things before anything else. On a longbow, string and limb vibration sound like just that. An arrow striking the handle or rest area sounds different and more violent.
Can you guess which it is ?
The bowyers website recommends 6.75" brace height for that bow. I wouldn't normally go less.
For a normal 28" draw, and split finger release, I would place my nock point starting at about 1/2" above level and nock beneath it. For a very long draw you may need to raise it up higher, even maybe getting closer to an inch, but I am just gonna guess that your bow / your draw doesn't require that high a nock point.
If the brace and the nock points are good, and I would check to be absolutely certain these are as you say, then we start getting into the arrow spine. Trial and error will tell, unfortunately some bows need way heavier arrow spine (I believe Black Widows are notorious for this) and some are not near so picky. I would take a wild guess and think the lighter spined arrows you mentioned should work best for that bow, maybe even a tad lighter yet, so heavier heads on those shafts might make them work. You say that they are woodies. Are they 11/32" diameter ? That makes a difference as compared to some of the carbons.
Is your bow / rest material showing any sign of contact ? Maybe place some fresh clean masking or paper tape on the rearward surfaces of the strike plate / rest area, then take one of your arrows and rub some stuff on it.. (shoe polish paste comes to mind), on the rear end of the arrow only, like, the last 6 inches, and see if it leaves a mark anywhere (for reference) after the shot.
If it does, where the mark is might help you guess better what is happening.
Lastly, you say your other bows don't exhibit this. What are their lengths ? Is this little guy the shortest bow you have ? Maybe the shorter bow is causing a smaller string angle, causing a bit of finger pinch, and a less clean release, that you don't get on the other bows.
So many things it can be, so you need to change one thing at a time and see what it does.
When you do, tell us what it was please.
ChuckC