One thing I'd like to say in OP's favour is that many Asberger's people have trouble with change. This is a strong symptom of Asberger's. Their disability requires them to do the same things at the same time every day. Change, no matter how minute, can cause Asbergere's people to have fits. Fits beyond their control.
The fact that OP is struggling with having to leave for work at different times every day (he calls it time management issues, but Asberger's people don't always express themselves the same way the rest of us do, so maybe he's really talking about change issues) tells me this may be a trigger for his Asberger's syndrome. So he may actually have a legitimate ADA claim.
(Regarding the constant calling his supervisors on walkie talkies, maybe a suitable accommodation would be to lay down some rules - for OP specifically - about what sorts of things he may call about and what sorts of things he may not call about. This might make OP's work life a lot easier. And I don't see as how it would be an especial hardship on OP's employer to write out some rules about this.)