Steve,
I rooted and potted up my figs in a similar fashion last spring and enjoyed the greatest success yet in getting little trees out of cuttings. In fact, I was probably even less persnickety about the process than what you described. I used rooting bins with Pro Mix HP. Once the cuttings showed roots longer than about 1/2 inch, but not much longer if I could help it, I potted them up to 1 gallon containers, again using unadulterated Pro Mix HP and buried them as deeply as the cuttings allowed or with only about 1/2 inch of the cutting showing if I could get them that deep. I placed the pots in clear plastic bins and left the lids ajar so air could circulate. As you get only 6-8 1-gal pots in a given bin, I ended up running out of space and took the potted cuttings with no leaf growth and little wood showing above the soil line and placed them in my garage without any protection (garage is attached and it was probably early April by then, so garage temps would have ranged between 50-70 degrees most days). I would be okay using 1/2 gallon containers, but I didn't have any, so the gallon containers had to get the job done.
I occasionally added some water to the pots as needed over the course of about one month and removed the lids entirely once the figs inside showed obvious signs of strong growth. This took some rearranging of figs in the bins as some pushed growth faster than others, but it was easily the most successful I have ever been going from rooting to potting to hardening off without humidity to hardening off outside (just set the entire bin outside starting in full shade to dappled shade to afternoon sun within two weeks.
I didn't keep notes, but I'd estimate that I had about an 80% success success rate with this no fuss method and I have no doubt that some of that was due to letting the roots on the newly rooted cuttings get too long before potting them up. Roots that are too long are, in my experience, far more likely to break as you slowly pour soil around them than are the shorter roots.
For those with humidity concerns, Reno, NV is at 4500' on the eastern slope of the Sierra Nevada and is dry as a bone all year and even drier than a bone during the colder parts of the year in which rooting and hardening off figs takes place. If I can do that here, you folks from more humid climes should be able to do it where you live.
I'm following the exact same procedure again right now, though if I can find some tall, skinny 1/2 gallon pots I'll use those in order to saves space and pot up to 1 gallon containers in late spring/early summer.