Hi ambermsam,
You're not expecting figs for next year, or ? Are you getting rid of the tree ?
I would have left 5 trunks and trim them around 2' or ' above the lowest available limb, to still get some figs next year from those uncut limbs.
For the cuttings, if you bleach them, I don't see a problem. But ok, sometimes throwing away is the quickest fix, and when you're in a rush, that is the best option !
If the tree was mine, I would try to root 3 or 4, just for the fun of it (cut and trash the leaves). After all those would be inexpensive cuttings for yourself.