Gentlemen: How do you look when you're hot?

For that gauge in the top photo with a span from 120 to 250, about 185 is straight up. So I would not worry about running where yours is with that thermostat. My rule of thumb for unknown radiators, and for that matter, block jackets as well - they're dirtier than you think if you have not extensively flushed them with something strong like Thermocure ( easy )or muratic acid ( which takes a bit of skill. )

You could drain a bit of coolant and temporarily swap to a 180 'stat, see if it runs in the center.