1920x1080 is not an integer multiple of the game's base resolution (neither 320x200 nor 320x240), so you'll want to use a different screen resolution to avoid this issue in source ports that don't use integer scaling for everything. On a 1920x1080 display, the highest you can go while ensuring integer scaling is 960x600 (960x720 with aspect ratio correction). If your display doesn't accept this fullscreen resolution, you'll have to play in a window and use IntegerScaler to remove borders and insert a black background.
If you want the game to use aspect ratio correction, you should also change the sprite scaling setting in DSDA to "Doom format" (I don't remember where it is exactly, perhaps in the status bar/HUD options).
The ideal solution would be to modify the source port so that it always draws 2D elements at an integer multiple of the original scale, even if this means text will appear slightly smaller at fractional scale factors. GZDoom has extensive options for this (with separate sliders for menu scale, HUD scale, status bar scale and console scale). A short-term workaround is to upgrade to a 1440p (6x scale) or 2160p (9x scale) monitor, which don't have this issue for any 240p games :)