Calvin,
IMO being that its this late in the season, I would not up pot at this time. I would wait for dormancy and do a bare root repotting. I have several that need to be up potted (and bare rooted) currently, but I will wait until after dormancy.
That being said I have up potted successfully, anytime, under any weather condition, if not bare rooting. If the potting mix and roots are disturbed minimally, there aren't any risks to the tree or figs. I up potted several 1 gallons with developed figs earlier in the summer, and have already harvested a few figs from one of those plants (a Celeste). One of the keys is that the potting mix in the 1 gallons are the same as the mix in the new container. The only thing that I do with the up potted plant is place it it partial sun (shade) for a few days to give the roots that were at the perimeter of the pot a chance to recover, then they are back out in full sun within 4-5 days. If you are not bare rooting and you have 1-1/2 to 2 months before dormancy, you could try re potting now.
BTW, thanks for the feedback on the Espoma fertilizer, I've observed very healthy growth in conjunction with the Dolemite Limestone. I have also noticed that the second year mix is even better than freshly mixed, so I have created a "mix heap", similar to a compost heap (pile) to allow my custom 5-1-1-1 mix to weather and age. Its currently being completely colonized by earthworms.
Several cultivars have not stopped growing, although they had put on lots of figs. From my observations, if the plant is given enough water and balanced nutrients and has a healthy developed and growing root system, they will continue to grow, while ripening figs. I have been pinching figlets on Conadria, Hardy Chicago, improved Celeste, Celeste and several other cultivars throughout the summer and MG fertilizer was stopped before the end of July.