Never heard anyone tuning their git to G-B-D, except when tuning a 6 string, D-G-B yeah, but then to do what you say, all you have to do is string it up lefty if your a righty to get the B-G-D.
Something new to play with I guess, but for the most part, people are use to having their base string at the top of their neck, and as far a thumb use, a common practice for eons, me personally, I have enough challenge with my stubby short fingers and keep my thumb on the back of the neck, so I'll stick to conventional.
Welcome anyway, and not squashing new ideas, just wouldn't work for me.
I have short fingers and using the thumb wasn't ideal on a 6 stringer, but a 3 or 4 string CBG should be possible. We just have to adapt and teach us old dogs a new trick. Haha
Sometimes I have a hard time getting the smaller string on the bottom fretted good, so putting the fatter strings on the bottom could be better. I'll give it a try sometime soon and thanks for your suggestion.
On a related note: I sometimes tune down the highest string on my four-strings half a step (from G-D-G-B to G-D-G-Bb for example) to achieve a similar but less complicated effect. This turns everything to minor while it still allows for playing major chords with very little adjustment (just fret the higest string one fret further up than usual...). This does, of course, also work with a three-string tuned to root-fifth-minor third.
For barre chords I use the index finger for G-D-G and the third finger for the Bb string. But I mostly use chord shapes on the four-string and for that whatever finger is on the highest string just has to move up one fret...
My reason for using this method of tuning down the highest string half a step is that in standard open tuning I have a hard time fingering some of the minor chords in a way that I can strum all four strings. The chords just sound a lot better with all four strings strummed instead of just three and I don't have to mute the lowest string with the thumb which often leads to buzzing sounds when I strum a little more vigorously... and I can play in G minor without fretting anything (I love G minor...)