Very simple 3-liner mod that changes Burner Mining Drill resource search radius to have it reach 1 tile around the thing instead of right under itself only, so that it can mine-out stuff from under surrounding inserters and belts, just like electric drills would do.
Uses same blueish radius visualization as electric drills have.
Does not change anything else about these drills.

Idea is to at least not need to replace self-fueling burners on small coal patches until area they were placed on is clean, which they don't do thoroughly enough by default, leaving ore all around them.
(tip: burner inserters can balance coal from drill to drill directly, chaining them into a neat self-sufficient line)