Okay, we're making progress! DOSBox staging, output=texturepp and texture_renderer=opengl. Forced vsync through NVIDIA control panel for the program. The game runs fine now when you're actually playing (which is great!), however with these settings the music skips in the menus, along with the menu screen stuttering in general. But we're getting closer...lol
Glad to hear that some progress is being made! I'm not sure how you've set some of the options, but with output=texturepp, all other scaling options should be disabled as it can interfere with how the pixel perfect scaling mode works. That could add a bit of lag if some are enabled. So to be clear the following should be set like this:
fullresolution = desktop
scaler = none
glshader = none
You could also try playing with the settings in the [mixer] section, "blocksize" specifically.
As for the VSYNC messing other games.... You had mentioned trying different DOSBox builds, did you try the DOSBox X one I mentioned previously? The VSYNC is built in, so that you wouldn't need to force it. Also you can get the pixel perfect mode through an OpenGL Shader, and I've updated that guide to reflect this.
EDIT: The only other thing I can think of is running the setup.exe through DOSBox and making sure that the PORT,IRQ,DMA for your audio choice all match what in the "dosbox_epin.conf"