Hey Brian, glad it is done and came out OK.
But I do want to post my two cents anyways, as there is a real simple solution (inexpensive, safe, fast & leaves perfect round hole.)
First, think about what makes a round hole -- a drill does not do that even though for most pratical purposes, the roundness of a drilled hole is usually good enough. A normal twist drill produces a tri-lobular hole in thin materials (for the sizes involved, a guitar top would qualify as "thin material" and render this defect.)
Files, rasps, sandpaper can enlarge a hole, but the effort vs results don't make it an attractive choice for this particular job.
Straight reamers are used to to make a precise round hole, don't use the tapered reamers where the goal is not to have a tapered hole. And that 90 degree countersink shown above (in reply #13) is really not for hole resize, it is only for prepping the entrance of an existing hole, like you'd do to use a flat head screw flush to a surface. (FYI, standard screws have 82 degree countersink, metric use 90 degree, but there are a lot of 60 degree countersink cutters for lathe centers, and other odd sizes that might not match your fasteners.)
Straight reamers are the hot $hit for sure on a lot of guitar tasks, and I use them for sizing tuner holes, T-O-M bridge / stop tailpiece inserts, etc.. Because they are available in practically any diameter, you can get a perfect size and shape where that's critical. And it is possible to find a carbide version from a surplus seller, if you have some luck shopping around for bargains.
That said, I do not use reamers for this common task of changing from metric import 8mm bushed pots to standard 3/8" bush pots.
My preferred cutting tool for this is a modified step drill, but I would start with one that is a little different than those that Vinlander posted image of, because you will need longer steps. Fortunately, the very cheap set from "Harbor Freight" contains one that works great, but you should cut the first two steps off of it. That modification makes it useable in thin semi bodies (you do not want the bit to cut a hole in the back!) To shorten the step bit, chuck it up in a high speed drill, and then use a cut off wheel (in another tool) or a file/saw/your choice of weapon to make that cut. Having the step drill turning while you cut the end allows for a more even result.
Now you have the 5/16" step that is a good fit as a pilot into the original 8mm pot hole, and this keeps the next step's 3/8" cut well centered.
I'm usually really particular, want to build jigs & fixtures to hold stuff, prefer to use the drill press over a hand held drill, and like to use high quality cutting tools whenever possible -- but this cut-down cheapo step drill really works so well for this task, leaves a very true round hole and I've never chipped a finish. I did buy some extras for backups, thinking the first bit would get dull, but to date I've not seen any degradation after retrofitting many guitars. You want the step bit with the longer sections, Harbor Freight puts one in this set of three they have on sale for $5.99 frequently. The 5/16" step works as a pilot, the 3/8" step leaves a clean, correctly sized round hole in just a few seconds. If you have a deep enough guitar, you may not need to shorten the bit, which makes this a really simple solution to a common task, and your guitar's new electrical bits will fit more securely.
John



Rialto Archtop Guitars UK
Today, 07:04 PM in Guitar, Amps & Gizmos