Well, I just very quickly got into an old unused session and put amp room on a dry signal. The clip I attached is as heavy as it can get, which will not be enough for some people. Mic position is pretty much on the speaker cone.
You've given me the impression from other posts that you're pretty experienced. So I've got a feeling you won't be happy with the Gtr Rig 3 amp simulation, but as I've said before the effects are really fun.
A combination of GR3 and an amp simulator would be my pick, if it's affordable. You could always use distortion pedals in GR3 without any amp or cab sim, then insert a quality amp simulator after it.
Apologies about the clip quality but I didn't have much time.