I have a Nesco dehydrator, I know someone who uses a convection oven @130f though. If you are eating them right away then you don’t have to dry them out all the way, just keep them in the freezer.
Looks like you maybe have English BT… Mine don’t usually get that dark on the outside but have a light interior like that. I use lots of biochar in my potting mixes, compost too, the figs love it. I only had a few ripe figs so far from my trees growing in compost socks, but they were very high quality and I think it was the compost. Mixed in biochar to a few but I haven’t noticed any difference yet.
You should get an Etna type, Hardy Chicago, MBVS, Gino’s Black, Black Greek, etc… They resist splitting really well and everyone loves the flavor.