Step 1: Disassembly
1) Any pieces (most likely just the front folding stand) that span both sides of the hot glue gun will need to be removed. Usually these just pry off-be gentle and they should pull out just fine. Get one side out first, and the second side should come out much more easily.
2) Remove any fasteners that hold the two halves together. My hot glue gun had Phillips head screws along with one triangular drive security screw. My handy dandy security bit set from ye olde Harbor Freight had several different size triangular drive bits. Triangular drive screws don't seem to want to be used more than a couple of times, so apply a good amount of downward pressure to keep the bit from slipping and stripping it out on your first go.
3) Set the glue gun on a table or bench and carefully pry it apart-you want to see how it goes together before you pull it apart and scatter the pieces. They aren't terribly complicated, but it is certainly handy to see how the spring is oriented and how the mechanism is set up.
4) In my case, this is where I pulled off all the glue from inside the gun that had gotten everywhere it wasn't supposed to when I put the ink pen beyond glue stick and into molten hot glue. Withdrawal of said glue covered ink pen out the wrong end of the gun left a pretty good mess of glue where it out not have been. Not shocking it didn't work right after that...
Step 2: Time for the Hot Rodding
1) Using a rotary tool cut a shallow hatched pattern into the feed ramp. This is the piece that pivots up into the glue stick to feed it forward. I turned a cutter to about a 45° angle to cut the grooves. Cutting the grooves actually pushed a little bit of the material above the surface that was slick, so not only did it tighten up the tolerance but made for a grippier surface to push the glue stick.
2) Reassemble*** and now you can feed even the slickest of sticks through your hot rod hot glue gun :)
***If your hot glue gun had a security screw now would be the time to replace it with a plain screw if you wanted easier future access to your hot glue gun's innards.