I don't really know of any "public" skeet fields around eastern nc, other than the one at Camp Lejeune. Might have better luck finding a sporting clays range.
You're correct about the gas systems on the Brownings and SX3- the same. Beretta 391 is nice but I thought it had more felt recoil than other gas guns I shoot. Have not shot Maxus or Franchi you speak of so cant speak for recoil but I know Franchi's are generally a light lot.
My main waterfowling gun is the SX3. Never a problem and extremely reliable, including many Sask. trips where the dust is so fine it will stop most autos without daily cleanings. Very soft shooter, and can be made to fit with shims that allow for diff LOPs and casts of the stock. I know and hear of lots of guys that shoot same gun and you just don't hear any complaints. Newer Golds and Silvers same way, just offer a few different features from the Win. Hope this helps some.
Locked and Loaded Super "Gauge" SH