Others have done more than I, but if I may offer what worked for me:
Make sure you know the 'look and feel' of your good fitting barrel & action when it locks up, use it as your standard to judge the new one. Remove the ejector/extractor per the FAQs so it isnt throwing you off.
Seat a cartridge in and see if the base is a tad (only a few thou. is OK) below being flush.
When the new barrel is on that edge of latching, if you hold a light behind it, can you see a gap at the top and it isnt 'square' with the standing breech? If so, it isnt seating fully down and the latch cant lock. At this point you need to determine if you can remove some breech face surface by 'spotting and stoning' (if the case base was low in chamber) or it it was OK you work on the underlug pivot.
If it is seating can you get a feeler guage in top and sides to check all around for equal fit?
Once the barrel breech and the standing breech are fully seated and square the latch should engage the shelf better, if not enough, now would be the time to stone the shelf slowly to get the latch taper to engage a bit more.
* If I missed something in this brief summary someone else should be here shortly *