So, to make long story short, I have a gas block that is supposed to be 0.625", and a barrel with a journal size that is supposed to be 0.625". Just ordered a new set of calipers to get the most accurate reading, but I'm suspecting that my barrel is a tad bit out of spec, and may be a bit more than 0.625". It's definitely pencil-profile in tapering, a 0.750" block just slides right over.

How can I best turn down the journal of the barrel (recall that this is a pencil-profiled barrel, and as such I only need to work with that 1.5-2" of length along the journal) so that the block slides over freely? Can I take an end mill on a hand drill and just ream out a slab of material directly opposite where the gas port is?

Definitely not.  Don’t do anything with an end mill in a hand drill.  Take a 6” piece of 1/2” dowel with a cut lengthwise about 1”.  Then cut a piece of sandpaper about 6” long by 1.5” wide and fold it lengthwise. Put the sandpaper in the slit in the dowel and chuck it up in your drill.  Now run that back and fourth through the gas block until it starts to seat on the barrel journal.  Once you’re confident it will fit, heat the gas block up to 200ish degrees and it should freely seat on the barrel.  Before it cools back off make sure everything is indexed properly.

@Coolmoney

Thank you for the advisement, helpful suggestion; just since I'm having a bit trouble understanding the orientation of how to insert the sand paper onto the dowel you described, can you provide a bit more elaboration using the numbered sketch I tried to put together?

Cut a slit in the end of the dowel. Cut a strip of wet or dry paper about  6” long and as wide as the slot. Fold it in half so it is 3” long.
Slide it into the slot so equal amounts are protruding on either side of the dowel.

or if you're not understanding the homemade sander instructions, just go to local hardware store and buy a 1/2" drill-mounted sanding drum on a mandrel.

Good practice is to work on the cheapest part. In this case, that's probably the gas block. Once they're mated, they're not likely to separated until the barrel is toast. If this was an out-of-spec receiver that didn't work with good magazines, that would be a different story.

Let me sketch it up for you.  The reason I don’t suggest using a dremel with a sanding drum is because it will be tough to maintain concentricity.  With the dowel method it will stay pretty concentric while allowing you to only remove a couple thousandths at a time.

Not sure if I’m able to post pictures but if you google or YouTube search “slotted split mandrel” or slotted sanding mandrel you will likely find better details than I can sketch anyway.  You will see jewelers use them a lot