For the past few years, I've used a totally different approach to 'pushing' film than I did in the '60s and '70s ( the bad old days of 'powerful' developers ). Today, the results are more pleasant, and are simple extensions of normal processing.
I use TMAx 400 ( in Xtol, 1+2, with reduced agitation ) at EI from 200 to 1600.
I expect that HP5 and DDX would give similar results, although I'd lean toward Delta or TMAX.
The agitation pattern that is efficient and safe would be 10 seconds every 5 minutes. A starting time would be twice the suggested time for a given exposure index. The results are very similar to a normal curve, as the the increased development time 'pushes' the shadows while the reduced agitation 'pulls the highlights'. Both Xtol and DDX are very efficient at maximizing whatever shadows speed the film has, and the result is a negative that looks disturbingly normal... with a tiny bit more base fog and - of course - a wee bit more grain.
It works very well in 35mm, so why not 4x5 ?
The trick is to begin with a film that tends toward a long straight line,
and a developer like Xtol or DDX.
HC110 and TXP, for instance, would be a different experience altogether ! But those 4 zones you got would be lovely !
Here are a couple of examples of the combination, from a tiny 35mm neg. The actual prints look quite normal, the scans lose so much 'presence' !
(there was a url link here which no longer exists)
(there was a url link here which no longer exists)
good luck
don