Using this spread sheet I was able to determine that all of the Van Door motors will, simply put, not get the job done in any sort of timely manner (6 seconds was the best I could get):
http://www.chiefdelphi.com/media/papers/2059
Go to the Linear Mechanism tab. Put in the motor specs at the top. Common specs for *previous* years' motors are on the first tab.
Using this spreadsheet, I was able to determine a 2008 motor, gearbox, and sprocket setup with a large (40%) room for error. The key features we designed for are current draw (which appears to be your problem) and "time to move load". If you consistently exceed the recommended current draw for a motor, you will eventually burn it out and/or see smoke. Where do you get the "recommended" current draw? Either from the specs or from experience.
Our final conclusion was to use a Banebots RS-550 motor, geared down to give us the lifting force of ~105lbs (way overestimated 35lbs to lift * 3 stage lift) without exceeding the 10A recommended current draw. Our backup plan is the Fischer Price motor.