Well, the problem wasn't what I thought it was, but I didn't actually get it solved for real until today.
My router (ESS + G540 + Super PID) wouldn't probe well at all. My mill (ESS + C10 + VFD) had no problem probing.
The difference? Router was running on a Windows 10 computer, and the mill was running on Windows 7.
Mill started having issues with probing the other day, after--quite coincidentally--the motherboard in my windows 7 box gave up the ghost and I swapped it for a slightly-less-old Windows 10 machine.
Light finally clicked today, and I went digging in that direction. Turns out that after the Windows 10 v1803 patch, Warp9 released a patched version of the .062 executable for Mach3 to resolve some DLL access issues that were preventing Mach3 from starting. This also seems to have had the side effect of fixing the problem with probing and G31 commands.
Anyone who comes across this when searching for a fix, go to the link below and download Warp9's version of the executable. Swap that out for the original one, and I'd be willing to bet that the problems disappear.
https://warp9td.com/index.php/sw/software-mach#MachThree