Memories! In 1 of my old jazz bands,I experimented with
mic positioning as I also was not satisfied with the mic-bridge position, I found the most natural tone by mic'ing either the left or right cleft openings on the upright which produced a sweet, bottom-resonating,acoustical sound. Another mic pos. I used was pointing the mic directly, halfway between the bottom of the neck and the bridge straight on. This produced a low,sharper tone. My role model when I started playing Upright,Charles Mingus,stated in an old edition of DownBeat magazine, that on some of his later recordings,that his preferred mic pos was having a mic behind the uprite as close to the body as possible with out touching,as the tone he wanted was a deep,hollow bottom, foreging note-clarity, to match the mood,flow and tonality of the music he was playing.
In short,the best advice is experimenation.Try as many diff positions to achieve the sound you are looking for.
BTW,what kind of mic are you using? And is the Upright fingered or bowed?