I can recommend Thornton's 2-bath as well. I only use HP5 and FP4 film, and the HP5 is alwys developed in Thornton's 2-bath. (The FP4 I usually dev. in Beutlers for even higher accutance).
I downrate the HP5 to EI 200. Not because I have made extensive EI tests yet (I planned to long ago, but never got around to it), but simply by default Thornton recommends such downrating. The compensating 2-bath works a little on the soft side, so the extra stop exposure only gives better shadows without causing problems with highlights (within limits, though!).
Dev time for HP5 is 5+5 minutes in 20 centigrades.
I use the "standard" B-bath as specified in "Edge of Darkness", so I have not tried other variants.
Agitation sceme:
Bath A : continuous 1. min, then 10 sec inversion each minute
Bath B : 2 inversions initially, then two inversions every 2. minute
I haven't made any careful studies of bath B agitation, but I have seen a recommendation approx like this: "as little as possible that does not cause streaking". Too much agitation in bath B washes out the A solution soaked up in the emulsion before shadows are fully developed. Too little agitation causes streaking.
I once tried only a couple of inversions initially, and then let i stand the remaining time in bath B. That proved too little. Then I just tried a few inversions every second minute, and it seems to work. I have stayed with this without challenging it further.
I like the 2-bath dev. becaus it seems to last forever (long shelf life, high capacity) and for its forgiving nature with respect to time and temp.
(I never bother to adjust the temp of the dev. bottles, I only maintain 20 centigrades in the darkroom where the chemistry is stored.)
Also, the dev. seems to give good accutance without the grain as prominent as high accutance devs like Rodinal or Beutler.
Thornton derived his 2-bath from an old classic from the 30ies, Heinrich Stöeckler's 2-bath. I've tried this, but I find the accutance far better in Thornton's variant.
I can wholeheartedly recommend Barry Thornton's book "Edge of Darkness". See the chapter "Stöeckler and colour blindness" for details on Thorntons 2-bath. (I can also recommend his first book "Elements" as well.)