This guns accuracy comes with two drawbacks. First obviously is the fact that it is a single shot. That means your unlikely to get a second shot in the close cover you mentioned. No big deal if the first shot was where you intended of course.
Second and more important is the weight. I assume you have shouldered one of these guns. If you have not, you should. In my opinion these guns are unnecessarily heavy for a close range woods gun. If you primarily stand hunt, then it is Ok, but i would not want carrry this gun when stalking for any amount of time.
Of course none of this matters if you must have a 20ga. As the Ultra is really the only choice there. But why not consider staying with a 12ga. That gives you much better options as far accuracy vs utility.
I don't want to get off topic here....so If you would consider looking at 12ga's and want more info let me know and I will follow up with my thoughts there.
Not flaming you, just adding some thoughts that happen to be different than yours.
Single shot is not too much of a draw back. Just think of all the black powder hunter out there. With the H&R's easy break action, ejector (not extractor), and maybe back-up shells on the stock with a shell holder, a second shot can come in about 2 seconds.
As for weight, I've heard complaints about H&R's and NEF's being too light to manage recoil!! Of course rifles slug barrels are HUGE. With a scope and extra shells, weight could be a problem.