Well, I tried doing this, and mine seemed to wrap fine.
I think it might depend on the font size you use as well. Maybe try a smaller size and see if it can bend more?
Also, it might help if you make the text arch before you do the circle? I'm not entirely sure, but at least this way you can see how much you can bend it yourself without the circle, instead of trying to make it fit.
I also put my text on two different arch layers. One bent 100% and the other bent -100% (or whatever they call it haha.)

i know it's not perfect and the bend isn't aligned very nicely, but it was just a rushed tester.
I do think illustrator would have a better tool for this, I don't have it installed currently, but it's been on my DL list forever. XD
I can try again later today, and if you still can't get it working, I can help you make the logo.
T^T sorry if this doesn't make sense or if it wasn't much help.