Jason, as you say, you haven't seen the inside yet, but I see no reason that it shouldn't be just great if you weren't already dealing with spoilage issues. I think the main reason to cut figs before drying them is to hasten the process, but on smaller figs it shouldn't be an issue. Of course, with mine, one out of four were sour, or moldy, or both, so I had to have a look (and a sniff) inside to make sure it was worth drying--and as big as the BTs are, they would likely all have rotted if I tried to dry them whole.
Martin, a few years ago I had some commercial figs that looked similar to what you show, and I wasn't wild about them either--but when I was a kid, my dad would buy bags of dried figs from some bulk food supplier in Loma Linda, California, and they were great. I would gobble them till I could hardly waddle. The cheesecloth would be ideal if your fig harvest corresponds with dry weather--free, and no limits on the amount of figs you can fit under the "dryer"!
Whether it's under the sun or in the electric dehydrator, I think the real key to success is starting with a high quality fig, and I'm sure hoping to end up with more of those in the coming years. I'd love to get a steady supply of dried figs anywhere near as good as the ones Dad brought home.