OK, I'm no luthier, but I always thought the body on a longhorn was shorter than a regular P, like the distance from the bottom bout near the bridge to the neck bolts, in order to accommodate the longer 22 fret neck. In other words, the Plus's neck is longer than "normal."
So, I don't know what body that J neck was designed for, but if the dimensions work, than you should be all set. I assume you already held the neck up to the bass to see where the bolt holes and nut line up.
Bit of a brain teaser for me. I hope it all works out for you!
I will be searching for "horny" bass bodies, but I'm sure you already have.