Hi,
I had quickly skimmed that and thought it led to a solution. (the previous help page they posted did)
I don't believe there is any help page for Apple IDs as AIM Screen Name Names suspensions. (it used to be with the single login you signed in on the AIM web site and could sort it from there).
I can only think that you have to get Apple to Intervene for you.
Call Apple Support (Apple Care) and say you have an Apple ID issue. (they are free to fix)
Level ones are script led and are probably not aware you can do this with an Apple ID.
Asks to speak to someone higher.
Explain that you use your Apple ID as an AIM valid Screen Name and that you think that the AIM side might have suspended the Name/Account and that dues to the current security checks that AIM have on the Apple ID check you cannot do it on the AIM site and can they sort it for you.
Remember the Level 2 may not even remember iChat (or even @mac.com IDs) and you will need patience to get him or her to the same point you are up to.
Unfortunately you cannot use an older Mac to reset this as the Apple/AIM duel login prevents those IDs being used in iChat 6 and earlier.
9:44 pm Sunday; September 25, 2016
iMac 2.5Ghz i5 2011 (El Capitan)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
iPhone and an iPad (2)