I've only done a bit of minor work to one: cleaning a lens; replacing mirror foam (important, if it is missing the mirror extends too far up, which will prevent the capping plate from latching correctly). But I have a couple of comments. If the shutter is capping, it suggests to me that the mirror may not be moving as rapidly as it should, perhaps, as it acts as the first curtain (so to speak) so, cleaning and if needed, lubrication of its mechanism may assist. Secondly, like their Exakta relatives they have a removable prism and top covers. So I would pop the prism out and remove the top covers to access some components, and take it from there. It probably doesn't matter with the Exas, but to be on the safe side, I'd recommend cocking the shutter before removing the covers, as it certainly does matter with an Exakta. One thing you have in your favour is that they are a basic and generally reliable design, so I would be fairly confident of being able to get it sorted.
Cheers
Brett