Ok, while the correct shimming is important and even critical, it is likely not a part of your issue.
It is, however, something that you may want to verify.
Nut-Shelling this, the shimming for this area is to pre-load the bearings (upper/lower driven gear bearings) as to prevent either outer race from spinning within the gear case!
The goal is an approximate .003" squeeze on the bearing, yet allowing the case to close the gap as close to ZERO as possible.
I'd forget the Seloc manual and the codes that are offered via OEM procedure. If the gears have been previously re-set, these codes are no longer usable.
This can be achieved by randomly "over-shimming"......, re-assembling without O-rings and just lightly and evenly tightened into position!
We then take an accurate feeler gauge reading between the two!
Then we reduce the shim pack accordingly, as to net this .003" squeeze on the bearing!
(you will need some additional random thickness OEM shims)
It's actually very easy to do, and it changes nothing to the gear pattern!
Running a RH prop places a "down-load" on the transmission's vertical shaft. This places the load on the top nut of this shaft (not the split ring), so this would eliminate an issue with the brass split ring washer/keeper.
Conversely, a LH prop places an "up-load" on the vertical shaft...... hence the split ring washer regarding wear!
You'd have to pull a transmission apart to see how the sliding sleeve and gear cup engage with one another. But "nut-shelling" this for you, once the friction between the sliding sleeve and gear cup begins, the self perpetuating force (from the steep spiral splines of the vertical shaft) further pulls the two together.
It would be unusual and unlikely that a sliding sleeve and gear cup were to let go once the thrust is applied.... but I'd have to say that this does occur, but rarely!
I have replaced a sliding sleeve in the past, that apparently corrected a similar issue.
The Borg Warner drive coupler and the actual gears are certainly not letting go momentarily.
Honestly, and without seeing this for myself, I'm somewhat stumped!
Have you considered trying a different "like" propeller as to eliminate prop slip, cavitation, spun hub, etc?