I’m sorry to say, I do not believe MS automatically entitles you to a reduction in hours, if those hours are the requirements of the job.
It would depend at least partly on why they are unwilling or unable to budge. Is there something that happens in that particular 1.5 hour-slot every Monday that would be difficult or impossible to reschedule, and the second-in-charge would be expected to attend, as a normal part of their job?
Other than that, I can only say that Monday mornings are an important part of the working week for most businesses - when objectives and priorities are set for the rest of the week. So they may not think it “reasonable” that a senior person would not start until 11 a.m. on those days. Perhaps you might have more chance negotiating the period after 4:30, than the period from 9:30, but I accept that isn’t what you want.
“Reasonable adjustments” have to be reasonable for both sides - it doesn’t mean that whatever you want, you can have. If it is a requirement of the business that a senior person needs to be there during that period, they can’t be forced to accept an applicant who wouldn’t be.
I don’t think veiled threats you would have a relapse and be on long-term sick if “forced” to work those hours is a brilliant gambit either. It might carry some weight if you already had the job, but as you haven’t, it’s not a strong negotiating tactic. If a would-be applicant says fulfilling the terms of the post would make them ill, my reaction would be: “Well, nobody’s forcing you to go for that post, and if you feel the terms as set out would make you ill, then perhaps you shouldn’t?” It also might make them think it’s borderline whether you could manage the job even IF they reduced the hours, as threatening you might be “out for an unknown amount of time” over just 90 minutes a week does call into question whether you could do the job at all, if you would be working that close to your limits!
I know this won’t be what you’re wanting to hear, but I think hinting “bad stuff would happen” if you don’t get the promotion exactly on your terms is the fastest way to make sure you don’t get it at all.