Thanks for the compliments, everyone!
@joey: I guess I'm starting to see the potential advantage of your approach - you wouldn't have to juggle quite as much. I suppose I can give it a try sometime in the next couple of days and see if it helps or not.
I suspect I won't get as much out of it as you would, since I'm not very good at solving sighted with a BLD method. This is similar to that, except that you're not actually sighted.
Just give it a go

I just want to see if you can actually get similar times with it, at least.
This morning, I had just about convinced myself that your method would be better. But now that I've tried it, I'm back to my previous opinion. I'm disappointed, because for a few minutes there I was convinced this would take me sub-5.
I've made two tries so far, both DNFs. The first was a disaster because I got lost during execution; I think just because of unfamiliarity with the approach. The second one was off by a 3 cycle of edges, time 8:44. My memo time is significantly shorter - more like 3 minutes. That seems outrageously slow considering what little I have to memorize, but apparently it's still hard even doing that little, for me at least. Then solving is definitely more work. The worst is when you realize you have to break a new cycle, and you have to remember what you've already solved.
Still, I think it can be about the same speed, and I could see how some people might find this easier. I doubt I ever will. But I'll probably keep trying until I get a success, at least.
@Pitzu: I'm really looking forward to seeing the results of your plans!!
@RCTACameron: With this method, square-1 multiBLD is really quite straightforward. Especially if you do it my way instead of Joey's. You just store the results in long-term memory, and you're good to go. You can figure out how to get to square by feel, if you can't remember, and from there, the memo is just like 3x3x3, only less to remember. Because there is so little to remember for a square-1, I actually think it will scale better to multiple cubes than 3x3x3 does. I would say that for a small number of puzzles, like 5 or 6, I should be almost as fast with multi as I would be doing them individually.