A reentrant G tuning was the original Tenor tuning, and was predominant into the 1970's. Of course this was also when most ukulele players considered the Tenor to be an illegitimate ukulele. In effect, it was the first mainland design attempt to make a "little guitar ukulele".
It was abandoned because it was felt that the low G note was too low (look at all the trouble people have with that note in linear C tuning) and that the overall tuning was so low it lacked any sort of brightness. To illustrate, our "Heavy Gauge" strings are not heavy enough for this tuning. You always need a wound third, and the outside notes are more like a second string.
If you want a very mellow sound, often paired with a "booming" G note, you can give it a try, but likely you'll abandon it too. I'm not an expert on Lyle Ritz, but on what I've heard, he often used the Tenor like a deep rythym instrument to back a smaller C tuned ukulele, and it also seems everything was amped. Then of, course, you can tune anyway you like.
It was Cliff Edwards who hit the sweet spot on a Tenor - B flat. Victoria Vox tried to go there - her publishing company let her put out one songbook in B flat, and then pushed her back to C tuning.
It's a shame that so many people are afraid of an intermediate tuning. It's not such a big deal. The Tenor is an intermediate sized instrument. An intermediate tuning will suit it best.
