faucet removal has me stumped

I have an old stainless sink that I believe was originally a lab sink in a college, was re-purposed in my home as a darkroom sink, and now is being re-purposed as a utility room sink. I'd like to replace the faucet with a kitchen faucet - to get something that will have some height, but I can't figure out how to remove the old one.

As near as I can tell there is no tailpiece/locknut holding the faucets on to the sink....I've attached top side/bottom side photos. The hot and cold knobs have a single screw down the center...I removed that, but can't get the knobs off, ever tried a little force with a lever under the edges, but no go.

I've had the sink for 25 years, so I suspect the faucet's been in place for 50 or more.

Anyone familiar with this style? How the heck does it come apart? There hasn't been any dripping...so would I be smarter to leave well enough alone and just use the existing?

Thanks for any help you can provide.

Good job with the pictures.

Get a handle puller, available at most hardware stores. I am betting that there are mounting nuts under the handle.

Probably right Phish. Pull the handles and remove the escutcheon or nut under the handles and the spout from the top. then the valve should just drop out of the holes in 1 piece.

Thanks - I'll give that a go tomorrow. Appreciate the responses.