Doesnt sound like very many positoins to me. I don't really like sell stops on options because I never want to hit the bid if the spread is wide, so I just put alerts in on the stock prices.
So if XYZ stock trades above $X.XX you get a text message and know to open up a chart and make a decision.
I think 20 combos should be managable. If your just doing long puts, then your basically just short stock (-delta, -theta) and managing 10 shorts can be real challenging.
If that's the case you probably need to upgrade your hardware / software to watch 10 positions simultaneosly. If you want to close 10 positions in 10 seconds, I have two words for you: "sell market".
+1 to what kztrading said re getting an alert if the ul reaches a certain price.
if trading that many (that's not a lot) individual stocks is too much just trade industry/sector/market etf's. less stock specific risk and usually cleaner patterns.