I would be in favor of C2 morphing into A, at some point. I have experience with (also testing of) React Native (creating iOS/Android apps) as that is what we did in my day job - although I haven’t been a main developer. And older JS frameworks earlier. So any JS would work for me, although I am not a big fan of JS 
As note: I think that for this purpose, going the mobile app route, is not sensible as that will compound a lot of additional requirements/handling/maintenance.
Having said that: I am surely not a fan of the current HAML solution, but that is likely me not understanding its ‘secret sauce’?
Looking at the usage in our coop, mobile needs to front and center. Although I don’t have conclusive data, a quick sample of a small user base I could ask, most use either their mobile phone or tablet to do the ordering. Only our treasurer uses his laptop for the financial/maintenance options. Many complaints do exist about the less than stellar user experience on mobile (which for us got worse when moving from the Adam fork to the main project).
So any language (I am not familiar with Turbo and only limited with Rails at this stage) which is able to create “mobile first responsive” experience would be fine with me.
I think that, again from our board and my tech perspective, we would be fine with a usable “old” admininstrator version (e.g. what is there currently) for the time being. Although we would welcome a transition to something nicer interface when possible, later.
In short: moving/redoing parts to new with an outlook of a complete (enough) overhaul in the future looks the most promising to me.
Edit: would it not be wise to revisit/improve the API regardless of which direction is chosen?