Looking at the data sheet for Ilfosol 3 (which I just picked up today!) it seems that pushing a film to 800 would result in about 28minutes of development? That's a guess, as I haven't tested it yet. I don't know if a 28 minute develop time would harm the film or not. That's a long time in the liquid I think. Perhaps you can't push it that far... I would guess it would come out with some kind of contrast problem... maybe WAY to contrasty. I personally like a lot of contrast, but you may not.
If you didn't want to wait around 28 minutes you could do it at a higher temp, but then your still waiting around about 20 minutes, even at 28c.
Now as for which developer I would pick. If I wanted to push 3 stops, I would try Microphen for maybe 16 or 17 minutes, as is.
HC-110 Dilution B at 11 or 12 minutes may work according to some research, as well as dilution A for 10minutes.
Hope that helps.