Hmmmm, i'm not sure the switchres utility will handle modifying modelines for Nvidia. Calamity will be able to confirm that, because I can't. If it's not going to work, you'll have to disable it in the .ini file. To try it anyway, open mame.ini and set super_width to 3840, and resolution to 3840x0. Leave the info screens on so you can see what mode the game runs in natively, and what mode switchres has picked/generated.
TBH i'm not sure what exact settings you'd want if the above doesn't work... it might not even work without a specific ini file for each game you want to run describing a resolution and uneven stretching in the x direction. Hopefully that last is actually possible. You don't need too many more modelines to run most games, 3840x240 of course, and x256, x288 mb. As above, leaving the infoscreens on will tell you what mode games run at natively, and you can add more when you need them.
If that doesn't work, you'll need to create each modeline you want to use.
GM might still be a good option as it has reduced input and audio lag.
Next, please tell me how you got that mode running on Nvidia? Did you really just type it into the CP and it worked? What exact card and OS?