The problem in my opinion with Partisans is that they are not so cheap. At 26MP per reinforce I find them too expensive to maintain alongside the rest of the army. With no shocks or heavy tanks in the doctrine you need to have a lot of stock units to actually have a strong army, and this leaves little room for expensive harassment troops. I would buff the commander by making the partisans cheaper to reinforce.
Could make em cheaper to reinforce, but ideally you sre to use them in a way that they won't take losses. The are not meant to fight in any fight they can't win. They are not falls or commandos even where they are elite troops that can also ambush. They are ambush troops and disposable ones at that. Iirc normal partisans are 210mp to call in, disrupt supply lines and fade into the bushes. Lay some mines off the beaten path, ambush. If the enemy sends enough to actually find and defeat them the front will suffer. They are unconventional, but that's the appeal.
As for lack of late game, mark target combined with the fantastic Soviet lineup is more than enough. They want for nothing.