In the changelog of FastDoom there's a note that 640*400 Progressive works on a HGC and original IBM 5151 while 640*200 (I'm not sure if interlaced or progressive) only worked in emulators and was removed because it would not sync on the 5151.
My bigger question though is do Windows 9x display drivers have any control over what DOS does with the display when in full screen mode? I thought it just saved the states of all the registers and then let the DOS program do what it will, which is why full screen DOS doesn't work on a secondary monitor.
e: Using VxD services you can probably map the VGA region to somewhere else in memory and capture all the IO Port writes, but there's no built-in support for it and you will have to make a VGA register simulator (or copy one from DOSBox or 86box or something) to handle anything more complicated than standard Mode 13h. I don't have a Hercules card and haven't tested Herc9x so I don't know if DOS games which already have Hercules support work normally in that yet.