Yes, polarized caps could be used. Dirt cheap aluminum electrolytics should be fine. Ones I was looking at were about 8mm dia x 11mm tall. The cap that goes across the cell could be a low voltage rating and therefore physically smaller. I suppose there's a possibility of the caps on the first cell being reversed, but since the square wave drive is floating, I think it would tend to be OK. Just to make sure, it might be good to add a couple of 'bootstrap' diodes to the bottom caps (I'll try to draw this into the schematic, but they probably won't be needed).
The square wave drive can be a simple half-bridge that goes 0-5v or whatever. It will need two switches, so it can actively pull down as well as up. 50khz seemed to work pretty good, but my guess is you could crank that way up to optimize the losses between the capacitors and the switching loss in the square wave drive and allow for smaller capacitors. Since the square wave drive only needs to run a few amps, the transistors won't get very warm and won't need to be very big (at least compared to motor controllers).
I've been looking at using separate transformers for each cell for a long time. They could be used in a very similar setup. There are some advantages and disadvantages to transformers. With transformers, I only need one diode per cell, so half the diode losses and heat. This is a big advantage. All the caps can be a lower voltage as well and there is no issue with isolation. Transformers tend to be expensive, but I did find some reasonably sized/priced ones that can do over 3A.
One thing I'm not sure about is the regulation. A multi-output switching power supply that has all the secondaries on the same core will have good regulation from one output to the other. If you have a bunch of separate transformers driven in parallel, I'm not sure what happens. If the load on one is higher (lower cell voltage), I'm not sure if it will draw power away from the other ones since they don't share the same magnetic core.
Driving the transformers may be easier, since I can use the guts from an off-the-shelf switching power supply.