Still Life 1:

I've played around with DxWnd and Nvidia Inspector, and the latter works better for Vsync and making the graphics look better, but locking the original aspect ratio doesn't seem to work in either, despite being enabled. Any other way to do this, so everything doesn't look terrible?

I'm not sure I have understood you correctly.
You are running the game full screen (without DxWnd) and your GPU stretches it to your desktop, wide resolution hence messing with the original 4:3 aspect ratio: is this correct?

Yes

It's not easy to help you since you provided no information about your system (hardware, OS, etc.).

The game original resolution is 800x600 (4:3 aspect ratio) and your GPU is probably scaling it to your monitor resolution, stretching it horizontally. So you have to set your GPU to keep the original aspect ratio. If I understand you correctly, you have an nVidia graphics card, so I suggest you to open the nVidia Control Panel, click on "Adjust desktop size and position" and select "Aspect ratio" (you may also have to tick the option "Override the scaling mode set by games and programs").