There is a fairly critical shift adjustment procedure on these engines that few people ever do.
You may have noticed a shift handle adjustment slot behind the shift handle?
That is there to insure that when the handle is shifted into forward gear that the gearcase is or can be adjusted to full clutch dog engagement.
This is an adjustment that you can literally feel.
Rotate your prop/propshaft by hand in neutral, back and forth, several times to get a feel for the amount of drag on it. Nice and easy, right??
Either you or a buddy then place and HOLD the shift handle hard against the forward or reverse stop and rotate the prop/shaft again. Feel a difference?
That extra drag is from where the clutch dog has bottomed out in forward or reverse gear and is dragging against the gear.
This is an exaggeration of the adjustment for you just so you can get the idea of what to feel for.
Now, you can see where the pin on the shift handle lays in the detent (one of the three U shaped detents in that flat metal plate) in forward gear.
Adjust your shift shaft (using that slot behind the shift handle) assembly to where you can feel some of that increase in drag when the gearcase has been shifted into forward gear. Once you have adjusted and you can feel this you are now fully into gear and that issue you have experienced will not happen.
Disclaimer time..............since your gearcase has already been jumping out of gear there is no guarantee this will fix your particular gear and clutch dog set. It takes very little damage for this to continue happening.