With respect to your jam problems, almost all auto models suffer that problem to some degree. Although I'm not familiar with your model it sounds like something is gunked up in the gas system forward of the receiver, which doesn't allow everything to return fully forward for a good gas seal by the time you fire that quick second shot, so you lose the gas and the gun doesn't cycle. When it's cold out just a little oil turns into molasses. Try cleaning the gun thoroughly, clean off any residual oil near the gas system and shoot it dry. Might also be a weak or strong spring, depending on which way it's oriented it might need a little stretching or trimming. Trimming the spring might need somebody who knows what they're doing, unless you want to risk buying another.
While I enjoy a nice double gun as much as anyone, consider the ammunition you will be using before deciding on one. Most steel shot is tolerable from a recoil perspective, but the uber-hyper-mega velocity loads and many hevi-shot (and similar heavier than lead) shells carry a wallop on both ends. Also, based on your location I guess you hunt some in salt water, my theory is that an expensive gun always rusts quicker than a cheap(er) one. I have tested this theory over many years and have proven it to myself, to the detriment of my wallet. A corollary to that theory is that they sink faster than autos as well.
On balance, I'm a fan of autos for waterfowl although I shoot pumps and doubles with some regularity. Since you have a Browning, I would be sure to look at the new Auto 5. In addition to the guns mentioned, for the price I like the Remington 1187.
In any event, have fun shopping! Look at it as trial and error, if the one you fall in love with and buy today isn't the life partner you were looking for, a divorce is relatively cheap. ;-)
I see while I was tinkering with my post JimG posted good advice about cleaning, also some insight regarding the spring.