I know it's been a while, but I finally got around to trying again.
In the interest of making small changes, I used my formula from above with the following changes:
AP flour instead of the BRM (it's what I had on hand)
I baked at about 500 (the best my apartment's oven can manage) on a stone.
I used a locally brewed Scottish ale for the beer.
Unfortunately, I screwed up my shaping schedule, so it didn't laminate very well.
However, it did come out with a nice flavor, with something like the "crunch" (and structural strength) I was looking for.
I plan to try again soon, this time getting my schedule right to see if that will make the lamination I'm looking for.