Hello Ed Davor,
I have done quite a bit with pushing E200 to extremes, all the way to 4 2/3 stops. The amount of exposure compensation increases with each stop, so it is not linear. I have spoken with some Kodak engineers to try and share my tests, but they don't want to spread the word more due to being unable to guarantee results. There is definitely more tendency to go bluer, so less need to use strong blue filtering. I often make do with just an 82A or 82B.
I have also used 320T to 2000, and numerous rolls of P1600, all the way to 3200. Of those two, I got my best results with P1600 at 800, which is actually a push at the lab. I almost felt that 320T was too blue in nightclub images, nearly to the point of needing light orange filtration. Some musician stage imagery I shot on P1600 and E200 (both at 800) convinced me to just stick with E200 pushed.
The Kodak reps last year gave me some Portra 800 to try with push processing. I sort of agree that if it is only 1600, then maybe just underexposing and processing normally might work better. Going up to 3200, then Portra works nicely, and seems like a viable replacement for P1600 (which is now vastly overpriced). My other issue with Portra is that the lab that does 90% of my processing does not push negative films, which means shipping out pushed Portra, often not a good choice for my work.
Kodak E200 is a quite amazing emulsion. I wish Kodak would also make it in Readyloads. There was some thought that it might get updated to finer grain structure, but now maybe less likely. It is medium contrast, so pushing still leaves it at acceptable contrast levels.