How to remove this bathroom faucet

I am trying to replace a bathroom faucet on a pedestal sink, but can't figure out how to remove the faucet handles. I'm pretty sure the handles must come off from the top, b/c the retainer rings below can't be removed since the fitting underneath is too large. There is no set screw on the handles and I've tried suggestions seen in other threads and nothing seems to work.

Anyone have any suggestions on how to get these out? I really don't want to have to take the sink out. But if I can't figure it out, I'll probably pull it out and use a cut-off wheel.

The reason for replacing is that the cold faucet is completely frozen up. We have very hard water. I'm thinking this could make the handles harder to remove as well. Anyway, here are some pics. If anyone knows anything that might help, please let me know.

Thanks!