I don't stealth much anymore, but I'd get omni's for the reasons you mentioned. You can't avoid crowd chatter when you're stealth taping and omni's will indeed help with the phasing effect you hear. The fact that you're at a rock concert helps because the music volume helps mask background noise. The deep bass you're after depends on the mic model/brand more than the capsule type.
Yes, you hit the nail on the head about standing too close to the stage. Standing really close to the stage can be really rewarding when the conditions are right. You can get a pure sound with great instrument separation. That said, recording stage lip usually frustrates me. First, if there are any vocals in the music, you won't hear them well on your recording because the vocals are routed through the PA...there are usually no vocal speakers on stage facing out towards the audience. So the insruments are nice and direct and the vocals are distant and full of room reverb. Second, if you're not centered well between all of the instruments on stage, one instrument can dominate your recording. For example, if drums aren't in the back, but to one side of the stage, it's going to be an awful sound...at least if you listen through headphones. Have you ever heard a recording that you can listen to for long if the drums are all coming out of one channel? It might sound the same as it did at the show, but that doesn't make for a good recording IMHO.