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A lot

Almost scared to ask, but... How many in the upper ranks?

I am not 100% sure but I would guess half.

Ironically this is the blockchain I've spent the least amount of technical time on. I'm assuming I could spin up a node and run a tcpdump on it and figure out all the IPs. Is it like other blockchains where there are a few pre-coded seed nodes and it just discovers the rest?

Yes. There is a seed node list which are usually not witness nodes. Technically you can get started with only one and pick up the others.