I did this one, with over 540 sts. on 36" circulars and it really wasn't a problem. It was a scrap/leftover yarn piece and the yarns were heavy worsted, worsted and some bulky. The needle size was 10.5 and it is approximately 60" diameter.
Yes, I think going up from 7mm to 7.5mm would help. The outer edges want to curl up if your bind off is too tight. So I just go up on needle size to allow for that.