Pascal, for that run I use just my thumb. (I assume you mean that thing at approximately :50 to :58 or so on my SoundClick.)
The notes on my SoundClick thing sound a bit "clipped" which I think is because I used poor quality mic and freeware to record it. They seem to "flow" a little better together live or on analog. I think a few of the subtlties don't make it through in the digital process with the cheap-stuff I'm using.)
Yes, Blake (and Jackson) did it with the thumb. They used what's sometimes called the "dominant finger" approach to playing, an "informal style" where the basic idea is you start with your thumb and index (your dominant fingers) and then just add your middle and ring fingers if and when required (in that order of dominance) to get any notes you can't get with only your thumb and index. (John, and Blake, used the thumb, index and middle to do it, the middle only occasionally in some places. John probably played it very close to Blake as he learned it from Blake's old "leader-boy.") They didn't use the more formal "assigned-finger" used in classical music. The dominant-finger style (focussing more on the stronger fingers) was more appropriate for steel-strings. (Although lots of great stuff is played on steel-strings by guys who were taught and use the classical approach.)
One thing both Blake and John were good at was using the thumb to be able to pick very fluidly in both directions, although it probably wasn't done in this tune. (Not by John anyway, and probably not by Blake.) (John used to always be "on me" about practicing back-picking with my thumb. He said it was a must to be able to play good Blake and "just came in handy" with some other guy's tunes as well. The last thing he ever said to me at the end of a phone conversation a few weeks before his death was "Give your family my love, an' keep workin' on that thumb now, you hear!" I'd practiced using it like that on and off for a long time and have a degree of dexterity with it, but since John's death I've been a slacker practicing with it.
Here's pretty much how I did that bass run. (I'm not tabbing it all exactly off the SoundClick using a guitar, just listening to it, but I know the 6 and 5-string notes are exactly like it's done there.
CODE
(Part on SoundClick at approx: :50-:59)
.D|--------------------------------------------------------------------------0----3\2p0-
.A|-----------------------------------------------------------------------------2-------
F#|--------------------------------------------------------------------------1----------
.D|------------------------------------------------------------------------0-------------
.A|--------------------------------------------------0-----2----3----0-1-2-----(2)-------
.D|-0h3-0h3-0h3-4---0h3-0h3-0h3-4---0h3-0h3-0h3-4--0-----0----0----0---------------------
(All thumb until about here.................................................^..)
I might have done this part... -0h3-0h3-0h3-4- ...picking both up and down with my thumb. It's not necessary to do that, but because I'm half-assed okay with thumb back-picking, I sometimes do it that way. (-^0h3-v0h3-^0h3-v4-- etc)
I know what you mean about having too "strict" a bass tendency when playing. I did(do) too sometimes, because after a long time of really trying to get my alternating-bass thumb together perfectly (like in purer Piedmont style tunes, like a lot of Bowling Green John Cephas' stuff and much of John Jackson's) it was hard to then consciously try to break the habit!

But yeah, Blake didn't let it define the way he picked. He used the thumb for alternation where and when he felt he needed to and that was it. Most times he used it more for percussion than actual picking-of-notes, except in something like a bass-run where the individual bass-notes are more clearly defined. He followed no picking-pattern, almost like some kind of free-form syncopation or something. He'd use his thumb (or any finger) wherever it worked best, like his thumb picking the note-pairs 0-0, 2-1, 3-2, 4-3 on the 3 and 4 strings, etc.
I was lucky enough to learn a bit about Blake from John, who learned it himself from Blake's actual "leader-boy" (I know I've said it before, but for anyone else reading this, a "leader-boy" was someone a blind musician had back then who in exchange for learning the craft from the blind musician, would lead him around doing things like making sure he didn't get hit by a car or a trolley, played on the best street-corners, didn't get his money stolen, and in general acted like a combination of a companion, a student and a seeing-eye dog all rolled into one!)
Anyway, I hope this helps a little more. Anything else feel free to ask, Pascal.