Entry/exit tactics for limited time availability

Due to my time zone (market is open 3:30am to 10am) and personal obligations, I can only look at the market during the last 2 hours and after the close. This means that I can only enter/exit stocks during the last 2 hours and/or utilize stop & limit orders. Using buy stops to enter will often result in whipsaw false breakouts, but is the only way I can really get in at the correct buy point for true breakouts. Entering during the last 2 hours of the market often means that I am entering late, sometimes several percent above the correct buy point, but I avoid the false breakouts that reversed on the day. What entry/exit tactic would you use if you could only look at the market during the last 2 hours and after the close?