I recapped the logic board with the polymer caps and all went well. The board pretty much looks stock with the polymer cans.
Some notes about recapping:
If you see a recommendation to twist, pry or lift off caps, don't do it. Even though there was some evidence of corrosion on my board, the leads of the caps were still firmly attached.
I used the cutting method. Cut the cap with a side cutter near the bottom of the can, and either pull off the remains of the aluminum can or cut it again in between the leads. Then cut or gently pull off the rubber seal around the remaining leads and then try to crack off the plastic base by "folding" it in half along the axis of the two pins. I was then able to desolder each pin separately. No pads were lifted or over-stressed. I used some flux (in pen form) to help remove the more crusty stuff and also with soldering new components.
To solder on SMT aluminum cans, I pre-tinned the leads on the component and the pads on the board. Then I heated the protruding pad on the board to make the connection.
The job is somewhat difficult since the leads can be hard to remove due to oxidization and corrosion. It takes a bit of patience and having the right tools to do the job. If you don't have a lot of experience, it might be best to have someone help you out who has done it before.