Who cut the wires on the remote? You probably could use a servo to push the two buttons on the remote.
Well, you're good at ebay That last switch look like one of those that requires considerable force to switch - mostly to be safe. I am just guessing. but it would probably be too hard for a little servo. If you like the servo idea then get two simply micro switches and do some mechanical arrangement. It is a bit Goldberg like, so the relay is still simpler. I think those relay modules are OK.
Could you post a picture of the label on the motor or copy the information on it over here ?These actuators sometimes have an "encoder" wheel, that sends a pulse per rotation of the motor or its wormwheel driving the shaft.If this one does not have that, you might be able to build it in yourself.This would probably be better than to use a potmeter.
Here's a really nice 3 position rotary switch that can be hooked up directly to the servo - cool!http://cgi.ebay.ca/ws/eBayISAPI.dll?ViewItem&item=121043185572