I think the best thing to combat this is to allocate yourself 2 spots (or one if you want to be conservative) to fool around with. You don't care if that person gets cut. And if you find yourself with an "uncutable" player, then it is trade time. I constantly manuever with an extra spot like that, always thinking about how I can improve my team.
Yes, you definitely let talent slip sometimes. But it only takes one "hit" against a fair amount of "misses" to pan out.
perhaps you pick up the hot 3b. the next in line for saves, etc. If they pan out, you have them as a tradeable asset.
I feel if you are depending on your bottom two spots on your team anyway, you may be in for a long season.