In any render mode except for Software, the characters disappear into the background and make the game unplayable. I would use Software mode, but then the menus run at about 10 FPS with input lag I don't experience in any other game on my system, as well as make the voice audio skip.

Has anyone been able to fix this? I've tried all the configurations possible with what you can do without hacking (checking Disable Hardware Zoom and disabling Shadows).

same problem here. game is unplayable in this state.

Yes I fixed this problem.

1- Download Klite Mega Codec Pack from this site: http://codecguide.com/download_k-lite_codec_pack_mega.htm
This fixed the problems for me.

Go here and follow the instructions:
https://steamcommunity.com/app/253920/discussions/0/490124466474674022/

I tried this solution and am able to play the game with acceleration and outside of software mode, the most desirable method of play. I also have the GoG version of the game, not the steam version.

Please read the following after reading the information in the link:
Note that within the instructions it states to copy two .dll files within the MS folder and to paste those two files into the Gorky folder. I actually had three .dll files in the MS folder. I did not know what two to copy, so I copied all three and had no problem. The thread in the link also mentions it being a solution for Windows 10; it also works for Windows 7, because that is the OS I use. Finally, this solution works with dgVoodoo v2.5, the latest version at the time of this post. Maybe one of the older versions will work, but I have not tried.