If I have a busy afternoon, with a houseful of under 5s, over 5s and a couple of over 8s, I can have a steady stream of parents collecting and they all overlap. I have suggested that no-one else is allowed through the front door unless someone else has left first, but they all ignore me!
If the parents are in a hurry, they will help themselves to the lunch boxes/bags in the kitchen, and will make a quick getaway. The older children dump their stuff in the hall, so that is also easy to "collect-and-go."
Most of the children I mind have been coming for years, so the parents have all got to know each other quite well. If there are lots of parents here, it's usually quite a sociable (and raucous) occasion. New parents have always been welcomed into the group by other parents (usually along the lines of "oh, you couldn't find a decent childminder either then!")
However, if I do have anything important to say to a parent, I will make sure that I say that I need a quick word before they leave.
None of that is particularly helpful to you (sorry!), but I would also talk to whoever was actually there first, unless it's obvious that one of them is trying to leave quickly. If you don't already do one, could you do a daily diary for the baby? I do one for my under 5s, so anything important/interesting/funny will have been recorded in there anyway, so you don't have to talk through the baby's whole day.