After looking into the b/w reversal documentation on Apug & Ilford, as well as the docs for the old T-Max kit, it seems that almost all of these suggest rating the film at or below box speed. Most films on the DR5 film review are the same with a few notable exceptions. Yet I can find 2 authorities which state a speed increase can be had.
"Low Light and Night Photography" by Roger Hicks states, "For real eccentrics, reversal processing of Tri-X and HP5 is possible with speed ratings of up to EI 3200 without loss of shadow detail; because it is a reversal process, it also tends to be finer grained than neg/pos printing."
"The Darkroom Handbook" by Langford & Knopf says, "you can reversal process black and white negative film, but rate it at three times its stated speed."
Who is right?