There are some very good 3 ½’ models that cycle lighter loads. The 11-87 Super Mag is a long way from being one of them even with the barrel seal activator installed. Good models would be the Beretta Xtrema’s, Browning Gold/Silver, Franchi 912, Winchester SX2/SX3.

If you go used you should be able to find all of these models in your price range. The Gold’s are being closed out in favor of the new Maxus and you may find a good deal on one. The SX2’s are being replaced by the SX3 so there are good deals on them. Franchi stopped making their 912 but is now made for Dick’s Sporting Goods called the Diamond 912 and is in your price range.