Does he have life insurance?
Does he have loss of income insurance?
At this point I think you really have to be working on the assumption that he is likely to die, through suicide or accidental overdose.
A better option may be that he is found out and loses his job, but obviously that also comes with a huge risk of suicide.
He sounds completely hopeless and desperate, and you sound totally paralysed. I assume you don't need me to point out how extremely high risk this situation is. He's not the type to think it'd be better for everyone if he killed you all and himself, is he? You're confident he'd only harm himself?
I assume that you know on paper it'd be better to force his hand, risky though it may be, than continue to do nothing. But I suppose for you, that if he kills himself following you taking action, that would feel worse than you doing nothing and him killing him self, even if your doing nothing actually increases the likelihood of him dying. That's the 'Trolley Problem' dilemma, google if you aren't familiar with it.
So, my guidance would be the following:
Go over again why he doesn't think the organisations set up to sympathetically treat doctors with addiction would help him, counter his responses where possible (call them anonymously yourself).
Check you've got life insurance and loss of income insurance.
Get in contact with Nar Anon.
Start justifying to yourself how you will rationalise things when he dies. (I don't mean that in a nasty way, but it will be easier for you and the children to cope if you've started some of this detaching process in advance).
(Obviously it would be much better if you can leave him, or somehow otherwise take action to support him. This is assuming that you won't).