I know I am answering a slightly different, more general question, but
I think it is quite crucial to learn how to unjam a rappel device without relying on anybody else's help before embarking on any kind of outdoor-rappelling adventures.
I have gotten my ATC stuck more times than I'd like to admit. ATCs don't just like to eat poorly assembled autoblock loops, they also like to eat loose clothing, and long hair (ouch!).
So here I go:
If you are rappelling on a slab, a jammed ATC is often not that big of a deal. You can brace yourself against the slab and, while you are "walking up the wall," you pull yourself up with one hand, whilst taking in slack with your break hand: voila, your ATC is unjammed. This of course is not possible if you are hanging in mid-air, unless you are able to do one-armed pull-ups on a 9mm "string." In this scenario it is nice to have a cordelette with you. You can attach it to the ropes above the ATC with a prussic knot and step into the loop that is hanging down, effectively taking the weight off your rappel device. If you don't have a cordelette, use a sling or a second prussic (I always carry two, in case I have to ascend the rope) and clip a sling to it, or, if you don't have that, you can use some of the rope below your ATC, that you will have to knot up a bit.
The bottom line, and you got that as I can tell from your post: practice all this when you are hanging at a safe distant from the ground. With stuff like rappelling, belaying at a belay anchor, etc, I like to go through all scenarios I can think of: what happens if I drop this, what happens if I used up all of those, what can I do if my partner fell off the cliff or is unconscious and attached to me, what if I can only use one hand, what If I can't use either of my hands (now there it becomes interesting!), what if I can't see a thing, what if the rope has a knot, is damaged, whet, frozen or muddy, what if the two rope strands have different diameters, what if the anchor I am rappelling from can just barely hold body weight.