The project management part, which I agree is the hard bit, could be made tractable too. Other orgs manage this all the time and build sophisticated software which continues to improve.
This is a booking management system for appointments, the initial problem statement is trivial, the difficulties lie in interfacing with other systems, simplifying UI, getting data in and out, providing some customisation but not too much, etc. These are all things you don't know how to do till you start using it.
The process you describe of getting 'domain experts' in a room to decide on a spec without contact with the real users then throwing it over the wall to build is fundamentally broken. You won't get to even 50% done without real users - that's the problem, and it sounds like that's what happened here.
You simply can't build a system like this without frequent contact with real users (old people booking appointments, volunteers entering data in a hurry, pharmacies who need to add extra info for patients), experts on the other hand will often add negative value unless they are trying to use it.
If there was a will within the org commissioning the work to appoint one project lead and then get out of the way apart from demanding weekly builds from week 1 onward this would be tractable. Collect feedback from real users and deliver every week. This is not rocket science and a small team could and should do it if allowed the space to do so.