Ithaca NID; Fox Sterlingworth; Ithaca Lefever; a fair number of German guns like Simson and various guild guns should all fit your price point. SxS shotguns seem to linger a long time on dealer's shelves and 16s have an ammo availability issue in the current market.
This little French Robust went TOO cheap. I wish I hadn't missed it, but I have one similar, a Robust No. 4 16ga. The Simpson Ltd gun is in better condition than mine. Someone stole it @ $550.00!
https://simpsonltd.com/fusil-robust-brevete-sxs-shotgun-d34041/