I know this is a remote possibility, but could you have your child support increased, to pay for a nurse to do the monitoring during your working hours?

I don't think it is remote, at all. I do not practice family law, but I would be surprised if a child's special needs were not considered.
Also, in our state, I beleive a handicapped child qulaifies for TEFRA services and there is a premium/co-pay that each parent pays based on income. This applies to non-custodial parents, too.
You might explore getting these services for your child.

I do not see how his running away is consistent with adoring his kids.

Alright, new problem. My WH had his interview which he said went very well. During the interview he found out that another job has opened up, a job perfectly suited for me that would probably triple my current salary. He's now trying to sell me on applying because, afterall, if I got the job, we'd both be making more money and living in the same city and he wouldn't have to be separated from his children.

Of course, from my end, I'd be leaving a small-town environment for city living and working... leaving a house that we have no equity in and for which we'd have trouble selling and even if we did sell would lose tens of thousands of dollars. I'd be uprooting our boys again (after moving three times in three years) to different states because of job losses by WH. And mostly - I don't want to follow my soon-to-be-ex-husband into another place where we'd work together only this time he'd be married or living with someone else... you know, the woman he REALLY LOVES. (What a win-win for him...having his ENs met on the home front and the work front.)

I am bound to get, what will sound like reasoned imploring, on his part and in the end, I suspect he'll blame me, yet again, for keeping him from his boys because I won't even consider applying for a job I don't want in a city I don't want to live. This will come, after my phone call to him of several days ago in which I told him that he'd be abandoning his children if he took this job and moved 800 miles away.

Please help me with my defense position.

I'd say you have just stated your very defensible position.

A house with no equity that you can't sell, or sell at a loss (I'm in the same boat, btw)? Dealbreaker.

Uprooting the kids again? AGAIN??? Dealbreaker.

(You don't have to tell WH that you don't want to be anywhere around him and his cake-eating ways, but that's also a dealbreaker to me!)

Are you comfortable where you are now? Stable, and in a good job? Then why leave simply for the lure of more money? The expense of living in a city would eat into that gain in many untold ways.

Sorry, but if he wants his job (and whatever "benefits" go with it), then he can have it. But he'll have to make the necessary sacrifices to see his boys.

Do not follow WH anywhere new. Leave that new town for him and his OW.

Even if WH was a FWH you do not move close to the OW.

Here is probably what I would say to him

"Honey. I love you so very much and would love to live with you and work at such a fabulous job BUT our marriage is in a crisis situation and now is not the time to make such a move. If anything, we should move as a couple even further from OW. Please know that I wish it were different with all my heart"