I've seen numerous left-handed Remington 1100's for sale here on the EE and elsewhere. IGA has a left-handed offering (not a well made product, unfortunately). Several manufacturers offer left-handed options.
For example, I bought a FAIR (Fabbrica Armi Isidoro Rizzini) competition U/O for my left-handed daughter. It comes in at $600 over the high end of your budget for this purchase, but I'm sure there are much less expensive field models also available in left hand.
It would probably be worth your while to surf all the manufacturers' sites and search for "left hand" or "left-handed". You'll see that there are more makes/models available in left hand, provided you're willing to order them and wait for delivery.