Assuming you’re using line-3x, 4x, or 5x with 320×240-optimized mode: have you tried (in the advanced timing settings menu) increasing H active from 320 to 348, whilst decreasing H backporch and/or H synclen? I’m guessing the H samplerate should probably remain at 427, but you or someone else should test that to confirm.
While I don’t have a Genesis, I do have a Playstation 1 and have used it with the OSSC to properly display PS1 games that output natively in 384x240p (Ape Escape, for example) by doing as I’ve described above (using line4x with 320×240 optimized mode). I’m guessing since the 348 pixel width you’re after is in between the 320 (default) and wider 384 active width that I’ve tested, 348 active width should already be possible for the OSSC. Whether your display will accept the multiplied signal (i.e., 1044×720, 1392×960, or 1740×1200 depending on the lineX mode) is another issue entirely