My scanner random disconnect issues started at several warehouses the moment 27.6 was pushed.
So after not being able to be onsite at the several warehouse locations, and trying to work with onsite to get a packet capture (unsuccessful), I ended up rolling back from 27.6 to 25.13 at one site and 26.8.1 at the other.
Several days have passed, and magically no more issues. >.<
This is a real bummer, as I was really hoping to make 27.6 the new stable code. And not being able to get a valid packet capture means Meraki support won't be able to do anything about it, so I have to basically avoid 27.X train for as long as I can at this point.
Hopefully someone else will run into the issue and also be physically onsite to be able to capture the issue first-hand so they can get a fix.