I went to Condomania.com and ordered the large condom sampler. Very instructive! You get a little sealed plastic containing about a dozen condoms of different brands and product names. I've been trying them on just experimentally. My girth is about the same as yours (about 6.25), and I found that the first three from the package that I tried on -- I don't remember which brands they were -- were impossible. I had the devil of a time rolling them down my dick, and the ring at the base pinched so tightly that it was difficult to maintain an erection. So far, the only ones in the bag that have fit are the Trojan Magnums. The Magnum regulars fit okay, but the XL's were the only ones with a positively comfortable fit. They did not seem too loose, either, since it took some pulling to get them off again.

The sum of it is that if you have a girth over six inches, even most so-called large condoms will probably be too tight for you.