Actually SGB, I think you might be projecting the very thing you're (gently) accusing Mal of - insisting that unemotional sex with a third party would be the best solution for this man, when it is evident from what the OP says that he doesn't want this at all. Like Mal and others, it doesn't sound as though he is someone who can separate sex from love. It's only the OP who agrees this might be a solution, but not him. He doesn't want to do this - and I respect that.
So, what gives? The kindest thing to do in this situation would be to broker a compromise. OP you seem to be finding all sorts of diversions from actually trying to sort this out, including having no faith in doctors ("what would they say?") and no time for counselling. All of this is obfuscatory behaviour and evading any responsibility for tackling this. I think we all do this from time to time, hiding behind our schedules or our lack of faith in professionals, to avoid doing something.
Your H has agreed to stop the lewd behaviour, which is great and long overdue. But like I said downthread, this isn't on its own going to resolve the underlying issue. He can't make you have sex and it doesn't sound as though you think that if you tried to have sex more often, it would help you to want it more.
So if nothing changes, he's got some very sad choices to make, but he needs to take responsibility for them, what ever they might be. If you do nothing to compromise, effectively you are telling him that he has got to get used to an impoverished sex life and if he won't have sex with anyone else, he will have to lump it. If he chooses to live with that, then he will have to honour that decision.
I still wonder, like I did downthread, if there is more going on than meets the eye here - and whether he is getting ever more resentful. I wonder where that will lead to?
Will he decide that he can't live like this and come back to you to tell you so, or will he give himself permission to have a secret affair with someone he can get emotionally attached to? The latter would be the irresponsible choice, so I hope that if he feels that he cannot go on like this, he tells you first. If you love him so much, I imagine you'd be devastated if he fell in love with someone else.
It would be so helpful I think if you both stopped making excuses for having a really productive conversation and booked some counselling. Some intervention now could prevent this turning into a fairly predictable, but sad situation.