My first check of a barrel is the cartridge in the chamber; ie, does it come flush with the barrel breech. This is important because if it was chambered a bit too deep you can, in this barrel fitting, also file the breech to get the perfect headspace while going for lockup.
Once that is addressed you would find it useful to pull the extractor/ejector out. It will 'get in your way' of this.
I take it you do not have another H&R/NEF to compare to? The barrel does sit down a bit from flush across the top with the standing breech of the frame. Until you get the barrel to that point you can go after it in a fairly aggressive, though straight and square, fashion. Once there. slow down. As you work it more you will see the barrel going deeper below that frame lip. This means the shelf is getting closer to the latch, BUT, you need to start being aware that you are not just going for lockup, you are also going for center hits on the primer from the firing pin. Prime a case, chamber it, hold the action closed and pop it off (if it will). You should be able to visualize what Im getting at; as you are bringing the barrel down closer to lockup you need to stop filing/sanding that underlug when you get centered primer strikes
even if it is not yet locking up.
If it does lockup, or is just starting to, you have a little fudge room to a tad 'north of center', but wouldnt you rather have it perfect?
So, with centered strikes, if it is not yet getting lockup, or not quite enough, is where I would want to start working on the shelf. I'll not go into detail on that yet as you have a good bit to go to get to that point, and yours may lockup at the right point anyway.
BTW, I may be your long lost twin brother from different parents
(current ride: '81 Yam SR500 cafe racer)