For upland bird hunting, you lose one round. One round is hardly worth worrying about, in exchange for a much better handling and shooting gun. While the loss of a round is a fact, I do not see it as a detractor in any way.
I have yet to see an accuracy issue with a double. I kill the same amount of birds, if not more with the double, with either barrel.
I suppose recoil could be an issue. I have never noticed it, but it is logical. I shoot a 20ga, just because the gun handles better. I went from shooting a 20ga 1100 to a 20ga double, and have not noticed a difference in recoil either way.
Im not arguing about the factuality any of your points, with the possible exception of the accuracy. I am simply stating that I dont see them as a negative. There are just as many reasons not to get an auto, or a pump.
Accuracy might not be the best word for it. Im talking about pattern convergence. O/Us are setup to have a point where the spread from either barrel will hit the same area. The problem is, with differing types of shot, or even powder changes will change the range at which this occurs. You might not have noticed it in your experience, but it is a bane to some shooters.
As for the 3 round maximum... I've seen and I have taken 3 birds with 3 shots. Never taken 3 with 2 shots.
Now the handling... we can go on for hours about that. Over and Unders handle better than what other shotgun? Are we talking an Academy $399 O/U vs a $399 Wingmaster? Or are we talking about a very high dollar O/U vs a very high dollar gas operated sa? If the latter, I have both and have never noticed one handled better than the other.
My best advice to the OP is not to blow your wad on your first O/U. I would start by finding a used one at a little less than what you are wanting to spend. See how you like it. If you find it so-so, keep that one and call it good. If you cant stand it, sell it. If you really like it, sell it and then save another $1k and buy a nice one.
I've got a Citori that I dont use, but I might have to do a tax stamp and make her into a toy.