It sounds like you're going to huge lengths to try and find a solution to this, and for this you should be applauded. I didn't mean to make it sound like you wanted to work your staff to death, I was talking more generally about if this sort of night nursery service was widely available, there would be potential for employers to do that.
The thing is, for me here I think there is a huge issue, as you say, of consistency of care. We all know that children thrive on consistency and routine - and whether that consistency is provided by the other parent being able to fill the gap when one is very busy, or grandparents, or a nanny, it is very essential to a child's wellbeing.
You say that the ebb and flow job is very exciting and has huge benefits in terms of personal fulfilment, and I support that wholeheartedly - however, that sort of ebb and flow will not suit small children as well, so whatever solution you find has to provide consistency for the children.
I don't want to sound defeatist, but in some cases (not all) there probably isn't a solution to the problem - if someone doesn't have a partner in a more steady job, or a nanny, or a willing grandparent, then maybe they have to say, actually, I just can't do this job right now. Without wishing to sound preachy, having children does force us to make some choices along the line, not all of them pleasant. And these choices have to involve the whole family's needs, so if Dad is a teacher and is always home by 4pm, then Mum can have a very erratic working life, iyswim.
I'm confused as to how some of the people doing this job can afford nannies and some can't, especially given that you uplift their salaries? Does this mean if they're the sole wage earner they can't but if they are married to someone earning a decent wage they can, for example?
With the best will in the world, I simply cannot imagine a scenario in which I would be happy to let someone I didn't know, no matter how carefully vetted, take my children home and put them to bed. Bedtime is a particularly difficult time, children are tired and clingy and need the security of a routine and a secure relationship with the person putting them to bed - Mummy suddenly not coming because work has got busy and being taken home by a stranger would be pretty upsetting for your average preschooler, especially if it's unexpected.
I guess (thinking aloud) if you could guarantee the same person doing it for each family every time, then the child could get to know them, but I'm not sure how you could work that so it was guaranteed.
Sorry to be very negative - without knowing what the job actually is it's hard to imagine it fully, but I'm struggling to see how it could work. And maybe I'm underestimating childrens' resilience, I might just be a bit precious 