If you're not willing to drop someone off your team, then there's not much you can do. If you have 1 or 2 players you can afford to get rid of, then pick up the best guy on the wire that is playing on Monday or Thursday to plug in for your guys that have the day off. Doing this, you could make up 1 game a week at 1 or 2 positions. I wouldn't worry too much about the C slot, but I'd try to max out your games in your other slots. Yes, you could drop your AVG a little (but 20 extra games isn't going to drop them much even if your guys hit .250), but you can gain in R, HR, RBI, and SB. Sometimes 3 extra HR or SB could mean a few extra points at the end of the year. I try to max out my games every year, because the award out weighs the risk.
Do the math and see how much 8-12 more R, 8-12 more RBI, 3 HR, 3 SB gets you (just a guess at what 20 extra games might be able to net you).
Ideally you want to use this strategy all year long so that you don't fall behind, and you can get an extra 50-100 games, which could make a huge difference in the standings (assuming you're somewhere around 10 games behind at each position slot and at each OF slot without using this strategy)