When most people who post here say they "like bass", they usually mean that they like their bass presented in a way where it is presented in far more quality than delivered in a neutral sound signature that reproduces the track as it was laid down.
If that is your meaning, the Grado and Senns won't work for you. The M-50 has recessed mids relative to its bass and treble, so it is probably not a good choice either. I have not heard the AIAI. You should also check out the Spider Powerforce, which can be had for $70 shipped.
I dis agree on the Senns. The Bass is really quite Neutral for the price point of $80, Some people want more, but For me I think it's quite good.
Out of his list, I must say the best sounding ones I've heard was the 558. (My next Buy). Everything else you said was dead on. Maybe I'm a Big Senn fan:)
I'd say if his budget is $200 Look at the 558. Then Buy some music with the left over $
I agree with you about your description of the bass offered by the HD 558, but I don't think neutral bass is what the poster is seeking.