Ok so, late reply (we just a snow flurry yesterday so of course I'm back on my snowmobile shit) but I recently rebuilt a 78' 340 invader motor. I used the aftermarket pistons and had the exact same issue that you are having.
I'm about to get A TON of flak for this, I know. But I went ahead and put the motor together. I set it up on my bench and put the pull cord on and just brute forced it past. After the first time, It got considerably easier (I don't even want to speculate why...).
I finished putting it together and it started up. I actually was able to run it most of the winter too. It had a radiator leak that sort of screwed me out of much of my riding it, but it other wise seems to be fine. I've started it twice this summer and done some grass rips with it too. In the near future I'm going to fire it up again.
Look,
I know how stupid that was. I really do. Do not ask me why I did it, and don't ask me why its working but it is. Motor still has great compression (145-150 both sides), turns over real nice w/ pull cord and runs strong (other than a carb tuning bog I still have to get worked out bc I'm a tuning scrub).
Video of first startup (smoke is because I waaaay over did the initial oil dose, plus had the oil pump geared up, plus had oil&gas mix in for the intitial break in)
https://www.instagram.com/p/BsOVdamA9HC/