I would do try for nap between first & second run if that doesn't work use the time between the 2nd & 3rd run, I think when you get to the 4th child you kind of have to run with what works & hope for the best. I suspect you will possibly get to the point where there are times that she/he has a cat nap after all the school runs are done
Although is there the possibility that you could get someone to help out with any of the runs?
In terms of bed time. The routine now has her with 12 - 12.5 hours sleep at night + 1+ hour nap, so around 13.5 hours sleep, so if she is only going to get a 35min nap then she'd probably need to have bedtime around 7pm to make the 13 hours with an 8am wake up.