I think I would want a counter balance spring on any garage door. I would expect it is time for a new door and hardware.

I'm sure the wood door in question has springs. If it didn't, you couldn't open it. The door probably needs maintenance which may include spring replacement or certainly adjustment. Once the spring tension is optimized, any regular opener will work. My mother-in-law has a pair of the solid wood doors as you refer to, and they both have regular residential remote-control openers.
I'm with you on the security aspect of these very solid doors, but they do require a lot of maintenance.

Saxman, after seeing pics of the solid doors, you are correct.

1. They have good looking counter balancing springs, from the ceiling down to the pivot arms.

2. They have good strange looking hardware pivoting arms 3-4' away, approx center of height.

3. They have been rebuilt and I hope with 3/8" ply vs 3/4" but they still used full 2X4s.

Seeing this I feel the doors will be fine with openers. They'll still have the option to install rolling panels vs solid doors. I built overhead storage cabinets above my straight "panel" doors (mid 1970s) before rolling panels became popular with openers. I have opted to stay with my straight panels (that requires less hardware height clearance) vs removing the storage. To add strength, I rebuilt the doors with 1/8" X 1.5" angle iron and added 3/8" quality ply. Each door is 10 - 15 lbs heavier and there has never been a problem with the doors. I reinforced pivots and greased as needed as well as original early to mid 80s openers. loger.