I'm glad lawnboy was able to clarify that Winchester low recoil loads aren't suitable for semi-autos. The Remington Managed-Recoil loads are a little hotter, so those might still work. Not sure though.
...I suggest you look at the Benelli M2 20 Gauge 26", The Beretta 3901 12 gauge in 28" or the Browning Silver Hunter in 20 Gauge in 26"....
...After further thought, I advise you to stay with the 20 gauge. In addition to lower felt recoil, they are much lighter and easier to handle. I will more than likely gravitate to the 20 within the next season or so.
I considered suggesting a 20-gauge a well. One reason I didn't is that I don't know of any particularly good 20-gauge guns in the $400-600 price range listed by the original poster.
The Brownings, Benellis, and Berettas will likely be about $800 at the cheap end and closer to $1,200 when you get into higher end models.
Also, there is nothing magical about a 20-gauge that makes it kick less. 20-gauges
typically have less recoil because they are shooting lighter loads. However, if you drop the weight of the gun too much, the recoil level comes right back up.
The 20-gauge Browning, Benelli, and Beretta have listed weights of 6.3, 5.8, and 5.9 pounds respectively. If you were to shoot the
same payload from a 6-pound 20-gauge and a 7.5-pound 12-gauge, the 20-gauge will have
25% more recoil.
...
IF, 12-guage Remington Managed Recoil loads cycled in an auto, those are essentially 20-gauge loads in a 12-gauge gun...
Even if those weren't an option, standard 1 oz loads out of the 7.5 lb. 12-gauge will still have marginally less recoil than standard 7/8 oz loads out of a 6 lb. 20-gauge.
Regarding the knoxx compstock that CLC mentioned, they are available for Remington 870s and Mossberg 500s (both pumps). I believe they are intended more for tactical weapons and turkey and deer hunting. The grip angle may not be ideal for wing shooting, and the heft of the stock may change gun balance a bit. Still, they do reduce recoil very well. I have one on a mossberg 500 and it tames 3" turkey shells and slugs pretty well, and makes target loads very easy to shoot. I don't know if it reduces as much recoil as they claim, but it certainly reduces it as much as any semi-auto I've shot. The compstock runs about $120 in addition to the $200-300 you'd pay for the gun.