I'm curious as to what you mean by : "but the 5/16 x 14 does not look to have enough of a piloted collar to fit the cue."
Does the pilot on the orig. shaft that you have contact anything in the collar or does it just hang in the recess? If that's the case, you could, for all practical purposes, use a 14 thd. flat-faced shaft.
There are very few piloted shafts today that actually use the pilot for it's intended purpose. Other than a very few exceptions, today's piloted joint is purely cosmetic.
The Predator BK2 would be an excellent shaft for your application. Swapping-out the insert is no big deal if done by someone who knows what they're doing.