Interesting use case! I also received your question via the online manuals form, but will answer it here.
The scenario is possible and works in our tests, also after a reboot. Each LAN port has its own DHCP client, therefore the 12Mic will receive separate IP addresses. It can be remote controlled on both networks at the same time via different IP addresses. This is necessary, because the ports are redundant (not switched) and therefore one has to be able to remote control the device from the network that one currently uses.
The IP addresses can be inspected via ['i'] (third button on standby screen) and then [LAN info] on the device.
A slow blinking ACT led simply means 'not much traffic', which is expected if you cannot reach the web remote. I would expect that if you check the assigned address, you will probably see a self-assigned IP address? This could be related to the way the 'airport express' (re-) assigns addresses. Also with static addresses, you would have to make sure that the airport express accepts the IP address. I think using an `Airport Express` is not very convenient, because it cannot be configured/checked from the iPad. If you connect the Mac with the configuration utility, you must make sure that you have disconnected from the PRI network port. Do you have a different WiFi router to test this?