I genuinely missed this post. Sorry.
This puts a completely different slant on what you need to do.
A lot of HR and managers lack creativity when it comes to flexible working. What you need to do is solve the problem for them.
You have a lot of knowledge which they will lose when you retire or resign.
Work out what you want, not just now but into retirement. Is it shorter days or less days? I personally dropped Wednesdays then Tuesdays and Wednesdays but I have known people go for 6 hour days I.e. they start early and finish mid afternoon. If you end up staying late dropping full days makes more sense.
Fridays are always popular NWD but Monday’s are better for leave and BH. Have a look how many colleagues currently work Monday to Thursday, if it’s most then opting for Monday means they can’t argue to few staff.
Your work load has gone up because so many work part time. This is not fair - what you need is a business case that illustrates the business is understaffed due to PT and they need to recruit someone you can train and develop to take over some of your increased work load and also cover on your NWD. Plus they can help cover the other PT staff on their NWD. This person could be PT.
Point out this allows you to do knowledge transfer before you retire and is good practice in business continuity and succession planning terms.
Yes there is a cost but point out if they recruit on the basis of FT and appoint PT they are saving salaries against budget. Plus if you drop a day they save 20% - It’s not quite that much. If you can do the headcount, FTE actual costs that strengthens your case.
Yes it’s doing their job for them but, as you say, they have painted themselves in a corner a business case where your NWD is different to most PT removes a lot of the argument as others are working on your NWD and can pick up the extra work like you do for your colleagues on their NWD
Sorry this is long
HTH