Another solution is to put a door lock back on the door. It would be easier to re-drill the round door lock into the door than to add handles back in.

In theory, all you would need to do is drill a hole in the EXACT right spot, install the lock, and then you can use the key to open the door, and the door poppers would open it the rest of the way.

The only problem is that there is a filled hole, possibly that has a piece of metal welded (and bondo'd), right where you need to drill- so it could be tricky.

Not an ideal solution- it kinda messes up the "smoothness" of not having handles, and you should probably look into getting the mechanics in the door fixed by a pro. But it's possibly the easiest solution.

One other thing: make sure the poppers are actually popping open the door. They may be too weak, and that might be your problem (you would just need to get stronger poppers). Or, the motor (or is it a solenoid?) to the door lock might need to be replaced. And lastly, re-lube everything. Its amazing what a little grease in the right spot can do.

good luck!