The adapter came in and the barrel plug fits perfectly. As expected, Mouser has some inconsistency listing the inner and outer diameters for their barrel plugs. When in doubt, check the datasheet.
Even better news: the adapter got my monitor working again. I'm really glad I only paid $30 for an adapter instead of paying $380+ for a similar G-Sync monitor. In case anyone's VG248QE with G-Sync stops powering up all of the sudden, check the external power supply.
Thank you, Sparky, for deducing the problem for me.