I've put a 27" wheelset on a bike originally equipped with 26" wheelset. It was a Sears Free Spirit, nothing special, but I wanted to try the 27s on something.

I made a mistake when trying the rear wheel in the frame, namely checking clearance with the tire fully inflated. Assuming that if the wheel didn't fit into the dropouts inflated then the frame must need to be trimmed for clearance, I trimmed more from the rear brake bridge and the chainstay brace than was really necessary, trying to jam it in there. After I realized that I'd never be installing the rear wheel while inflated, I felt like a real butcher. Just a word to the wise.

Can't remember if I had to change the brakes. They may have been slotted enough to move the pads high enough to match the brake surface of the new wheels.

The ride felt a bit smoother with the 27s, maybe because the longer spoke length soaked up bumps that would be jarring with the 26s?

Switching to 700 would give you the greatest variety of tire choices. I know nothing about 650cc, but the 650b size seems to have a lot of really devoted fans.