Pushing Film with TFX-2: More time, dilution, or both?

The Film Developing Cookbook gives guidelines for pushing 'modern' film.

With straight developer (not advisable for t-grain emulsions), add 25% or 50% more time for a 1-2 stop push.

With diluted developers, double the amount of water, then add 50-100% more time for a 1-2 stop push.

I'm assuming, as a compensating developer well-adapted to reduced agitation, TFX-2 would be categorized as dilute, not straight? So I'm inclined to go with the recommendations for doubling the dilution, adding 50% to time, and then another 50% for reducing agitation every 3 minutes.

Interestingly enough, the Cookbook says DD-X is the best developer for extreme pushing, e.g. shooting HP5 at 2400-3200—for reasons that are not entirely well-researched or obvious!

And, straying from the exact topic a bit, if you have any insight as to why the Cookbook insists that t-grain films have to be overexposed and underdeveloped in order to even provide decent results, by all means let me know. The writers note that, when shooting 35mm, one has to privilege resolution and sharpness or unobtrusive grain, when so much enlargement is expected of a negative. These fancy Delta/Acros/TMAX emulsions would seem to excel at resolution and sharpness relative to grain size, but the authors never seem to compliment those films at all.

I have not read the cookbook so I can only guess at the authors reasoning. I do push Tmax 400 and 3200, I've used Tmax developer and DDX which I think is a similar formula, Clayton F90, no longer being made. My last roll of Tmax 400 was pushed to 1200 and I developed in Acufine stock. Seems to me that folks who shoot "fine art" are looking for "best" shadow details. Over exposure for shadow details in zone II, the under developing to control highlights make sense. If on the other hand if your intention is to capture action, news, sports, street, wildlife maintaining a high shutter speed is more important than shadow detail you want a high ISO in which case box speed when possible then when push when needed, expose for the highlights and let the shadows fall where they may. I think Kodak over the years has walked the line to where they put box speed. In the very old days, 20's to the 70s, amature photraghers used simple box type cameras, used the exposure guide printed on the film guide. So the ASA was generally slower than the film actually was. Foma on the other hand seems to very liberal with box speed as their data sheets indicate that with most developers their film are really about half box speed.

I do not use TFX, but when thinking about pushing Tmax 400 Kodak's datasheet is detailed and provides times for pushing to 1600 and 3200. The push to 1600 is only a 1.5 mint longer than at 400 with Tmax developer. So a 20% bump for Tgrain from 400 to 1600, no change from 400 to 800. But you will need to test to find your personal ISO for film developer combo.

"if you have any insight as to why the Cookbook insists that t-grain films have to be overexposed and underdeveloped in order to even provide decent results,"

It doesn't. That was a rumor that was started on photrio and looks like it may run and run.

What it said , FDC 2020, was that overexposure and underdevelopment gives results like Panatomic-X with T-Max 100, ie tabular grain gives results like traditional grain if overexposed and underdeveloped.