Just got off the phone with Meraki support, was advised to disable Client balancing on the RF profile which could cause issues if the APs are close to each other (I'm not too sure about the layout on this particularily troubled site, but there's never been a wireless survey done there, that's for sure). There are just 3 MR42 APs running 30.7, scheduled for upgrade to 30.7.1 next weekend.
"AP unable to handle additional clients" is just the slightly misleading alert shown when clients are bounced off of an AP due to the client balancing, I was told.