ex3700 in access point mode needs internet connection - interferes with DHCP to other access points

The wifi devices connecting through the ex3700 receive all their config from the dhcp server as you'd expect. The ex3700 as a WAP is merely acting as a bridge between the wired and wireless worlds here. The WAPs IP configuration is (I hope - as it should be) only relevant to the ex3700 itself. I am merely setting it up so that the WAP itself cannot access the internet - which I could also do in the firewall but if the device has no configured gateway address it can only talk to its local subnet which is how I prefer to configure any device that should not require internet access.

You seem to have a very poor understanding of TCP/IP if you believe that the configuration of a bridge can affect the configuration of devices that are connecting through the bridge. The only way the EX3700 would be able affect client configuration is if it was acting as a DHCP server with clients also configured to use DHCP. The last thing I expect a WAP to do is run a DHCP service or even act as a DHCP proxy. This latter would only make sense if the WAP was also a router which is the last thing one would normally want of a WAP.

It does though appear that the ex3700 is doing something DHCP shaped as when it is on, clients (even those not using the ex3700) sometimes take a very long time to receive their configuration.

I would not even have suspected this sort of thing a few years ago, but I bought a small cisco managed switch a couple of years ago that some cisco idiot had decided to put some layer 3 'security enhancements' in, which totally screwed up nfs and some apple stuff. Cisco had to produce a new version of the switch firmware to fix it as the 'enhancements' could not be configured or turned off.

c'est la vie