There is nothing wrong with your Mossberg. Learn to shoot it, and rub it in the guy's face
Seriously, you would not believe the arrogance and attitude of many upscale clay target shooters. I have shot many rounds of skeet with a near-stock 870 and lots of trap with an 1100. One memorable day, I badly outshot a guy with a new $4,000 Beretta with my $200, pitted, drag-through-the-woods 1100 (I wasn't responsible for how it came to look like it did, bought it used and evidently someone put it in the case wet).
OK..... what you DO need for trap: First of all, at least a modified choke. Full is probably more common but modified will work on the 16 yard line, at least if you shoot quick. Short barrels make it more difficult, but it can be done. A 30" barrel with a full choke swings pretty well. Having said that, I have seen guys shoot 27 yard line with .410s, so it can be done with anything you can shoot.
Second, you have rising birds. Need to shoot HIGH. Most trap guns are set up that way so let's assume that's why you were advised to get a new gun. But, you can get buy without one. With a vent rib barrel, have a mid-bead installed (if you don't already have one). Then, instead of looking straight down the barrel, set your chin a little higher on the stock so that the beads "stack" in a figure 8 or so. Set the bird on top of the front bead, your gun will shoot high. Keep swinging after you shoot.
The last part is foot position, but won't be able to cover that in a post. Do a little searching and see what you can find. Mainly, get your weight more on the front foot, and feet open enough that you can swing the barrel either way.
A semi-auto will reduce recoil a bit, but annoy the guy to your right that you are flinging shells onto. There are little sheet-metal do-dads that attach to an 1100 to hang onto the hull. Not sure about other brands.
Good luck.