The attached TSR program sets up a 320x240 native resolution with an 8x15 font, yielding a 40x16 text display. Mode 1 is used as a base because the horizontal parameters are already in place, so only the vertical must be adjusted. The display is double-width and double-height to create a typical 60 Hz frame rate. The font is the VGA 8x16 font with the last line deleted. There is a chance this will work on real VGA, but I don't suggest trying it unless you like taking chances with your hardware.
You can put the TSR in the [autoexec] section of the conf file, or in the command line of the DOSBox executable, to activate the display at startup. If the display becomes deactivated, such as by the DOSBox shell CLS command that sets mode 3, just run the TSR again and it will reactivate without reinstalling itself.
Few DOS programs will adapt well to 40x16 text, and the DOSBox shell is no exception. However, if I understand correctly, your plan is to use purpose-built programs where you should have control over their use of the display. When the TSR is resident, your programs can activate the display by setting mode 1.