Although it never hurts to let them sit, I'm with Ben on this. I press my bands on so tight that they shave wood as they are pressed on. I ream them to 5/8" before pressing, and the reamer will absolutely take about 1/64" off the inside in the vicinity of the band when I ream them again right after pressing.
I'd suggest getting 1/16" brass rod from a local hobby store for use as pins. Cheap and easy. You sand/grind one end nice and flat, deburr it with sandpaper really quick and you're ready to roll. Go to McMaster-Carr's website and get yourself a 5/8" spiral reamer if you don't have one, get a 5/8" hardened machined steel shaft and make yourself a pinning jig to cradle the call with the shaft running through it. Drill using 1/16" a bit down to the shaft (you won't hurt it), insert your brass pins and drive them down tight to the steel shaft with a small hammer. Clip them off with wire cutters right by the band, then carefully peen the ends down with a ball peen hammer (don't use any other kind of hammer). Peening the end of the pin expands it out in the hole in the band and will result in the finished product being totally invisible if you do it right. After peening, put the call on your lathe's 5/8" mandrel and spin it at around 500rpm, then use a bastard file to remove the mushroomed brass from the top of the peened pins as the call spins. Then sand at 220 and go through all the grits to about 2000, then use Brasso or other metal polish on the lathe. Done right you'll struggle to ever find your pins in the finished band.
