I've taken the advice of some other forum members and pulled most of the leaves off my potted trees. 

It seems to have worked, which is amazing, because many of the figs are starting to change color. 

However, they are just getting darker, but not swelling.  Why is that and is there something I should be doing differently?

The other figs that ripened on their own a few weeks ago swelled first, then changed color.  These seems to just change color but stay the same size. 

      

The color may just be due to the extra light on the fruit. I don't think they will ripen without swelling first. Or if they do ripen without swelling they probably won't be worth eating.

And I'd remove all figs that have no chance to ripen, ie remove upper ones. I'm not a fan of removing that many leaves. I think it will reduce fruit quality.

when you say remove the upper figs...is it that figs normally ripen from bottom up, and thus the top are last to ripen?

cool, didn't know that.  I'm guessing it's because they get the sap, and thus nutrients, first. 

I'll take the top ones off. Hurts to pull of unripe figs, but gotta do it to save the rest. 

I am also not a fan of removing leaves,especially,in places like Texas where the sun is hot During Summer and cold during Winter.
In the Summer your fruits will be boiled (and can abort),before ripe and when Winter come your tree will be killed by cold because the plant did not accumulate strong energy in the root system due to ,not having enough leaves to ,capture energy from sun.
Removing leaves is a losing proposition,in hot Summer climates.