From experience with HC, I would not use dilution H to push that much. Even dilution B won't do it. It is near impossible to get an honest-to-god N+3 via development.
However, you only want to push as much as you need to get contrast and density to a *printable* level. It does not need to be perfect; just printable. You need not necessarily do a true +3. In fact, that might make the negative pretty hard to print. I would aim for a +2 at most.
On the plus side, it IS a non-random film, and it IS 4x5, and you ARE only going to 8x10 size. Therefore, it is not grain or sharpness that will be the problem.
On the minus side, you are using a film that does not have a ton of latitude, and anything that you thought would end up as a black or dark gray is now gone forever, all your intended midtones are now dark grays, and all your intended highlights are now midtones.
How many negs do you have? The best course of action would be to develop just one of them at first and see what happens. Pick the shot that you think is the least likely to actually be printed, as long as it was exposed like the other shots.
You don't need a new developer, nor will a speed increasing developer help you very much anyhow. HC makes a perfectly fine push developer in addition to its myriad of other uses. I would start by using dilution B at double the recommended time, with the realization that all you can do is try to salvage some midtones and highlights. Try to use 24C instead of 20C. It will make your time shorter, and modern films are designed to be processed that hot just fine. See what happens. It might be too much, and it might not be enough. You never know in such an extreme case with such a sensitive film. Try to print it, and make adjustments for the next sheet. You may want to not even push it that much and then use some Formulary intensifier and/or some selenium toner on the negs. This will make printing easier by giving you more density without totally jacking up the contrast.
