I think the big plus side to the pistol, would be using it as an organ (parts) donor. The bolt and springs in the P are already reduced in weight to accommodate a 6" barrel. If you compare the parts between your 15-22 and 15-22P you will find some substantial differences in the bolt. There is quite a bit of weight reduction for it to cycle correctly at only a 6" barrel. Plus the springs are different as well.
As a "stamp collector" you are already accustomed to dumping a certain amount cash to have the cool kid toys that you really want.

And since we aren't talking about mega $ for real AR stuff. If it was me, which eventually it will be since this is on my extended "to do" list.....
I would buy a new garden variety plain Jane M&P 15-22 rifle and do the SBR paperwork at 6". Then swap over the complete pistol upper you already have. When you take the 6" pistol barrel with a 5" suppressor it makes a perfect 11" overall. Then look around and acquire another rifle hand guard and cut it down to your desired exposure length and swap it over to the pistol upper. You now have the best of all worlds.
1)You have a pistol lower sitting unused, which you said you didn't particularly dig anyway, but it is still available to swap back and forth if the mood strikes you.
2) A spare complete rifle upper to set up for a different purpose. Put a red dot on one and a scope and bipod on the other, or what ever you want to do.
3) And a slick 11" internally suppressed SBR.
Just thinking out loud. You already have the YHM suppressor. You already have the donor M&P15-22P. So out of pocket it costs you $200 for the stamp, and $450 for the new rifle. Then it is all plug and play.
As far as swapping the suppressor over to another weapon. you can buy a blank fake can for less than $30 at cheaper than dirt. Put that on the SBR when you take off the real one.