This sounds like an excellent solution to me. It accomplishes what feels right to me (near-dead aliens being easy to stun) and avoids the stunned-by-actual-guns problem.
On suppression, I'm surprised you're suddenly having second thoughts. Going back to X1, I thought suppression was one of the clear major improvements compared to the original X-Com. It's a very useful tactical tool, you spend some actions that are unlikely to kill the alien but you weaken the alien for the next turn. Suppression makes them fire less on their turn, and eliminates reaction fire, so it's great for situations when you cannot kill the alien outright.
It mostly works the same way in the final version of X1, each bullet applies a (small) amount of suppression along its trajectory, and then I think a bit more around the impact point. So the trajectory suppression lets you suppress your own soldiers by firing too close to them, and the impact-point suppression means you're likely to suppress the target by hitting the ground in front of it with a few bullets.
I like gunfire suppression as well as long as it's a dedicated gun / fire mode. The current LMG is pretty good IMO with two fire modes, but the 10-round mode is a bit too weak at suppression and the 3-round mode a bit too weak at actual combat. I'd make the 3-round burst more accurate, boosting it in a direct combat role, and I'd make the 10-round mode more reliable at suppression, though I think the current 10-round burst is almost good enough at it.
X1's mechanics resulted in the occasional suppression from concentrated non-LMG fire, too. That doesn't really feel important but an Xcom-style game benefits from such rare interactions.