I'm not sure why Warmoth offers anything but a 7/8" hole for a side jack mount. The 3/4" (19mm) hole works with nothing, and the 1/2" hole supposedly works for the panel jack, but nobody in their right mind uses those, and they won't breach the depth on many rear routes anyway. The 19mm (3//4") hole is just a tad too small for a normal 1/4" jack, and re-drilling it is a major league pain in the shorts. You can try sanding it to a larger opening, but that's no fun, either. Tough to keep it round. If you wanna try it, get a plug to plug into the jack as it's mounted to the plate to check clearance. The tip connector has to displace about 1/8" when you plug/unplug the plug, so you need more clearance than you think.
The best fix is to get a short piece of 3/4" dowel and glue it into your existing hole so the face is flush with the exterior of the body, then re-drill it for 7/8". Use a Forstner or brad point bit - twist drills will likely wander. Holding the body still while you do that isn't easy, so be sure to think that through before you start. A large bench vise or a buddy who trusts you not to drill a 7/8" hole in his forearm while he holds it will come in handy.