Be certain that you need to relieve the hinge. I have fit dozens and dozens of barrels and have needed to "relieve" but one. I have had to square a couple breeches, and clean up some lug welds.
Is your barrel a ejector or extractor? When fitting a ejector barrel, I like to remove the ejector completely. You can also remove the trigger guard to "see" the relationship of the latch and the shelf.
Its better to look three or four times then to remove steel form the wrong place.
Many times on a stubborn fitting, I'll stop when it gets to be monitions. Then let it sit for a day or three. Coming back with a fresh outlook. Many times the problem becomes quite obvious. Just this afternoon, I was fitting the new heavier latch springs and found the the side of the latch was dragging on a bit of casting slag on the side of the receiver. The dremel made quick work of it and now I can see the much more stoning of the shelf would have ruined the barrel. Another time I just couldnt put my finger on the problem... I removed the extractor to find a weld was standing a bit proud and touching the inner sides of the receiver. I ground it down and finished fitting the latch easily.
CW