Ok... I am really glad I asked because this is much more complex than I saw from your first post.
The wireless capabilities come from 2 Ubiquiti Networks hard wired Access Points running WPA Personal.
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The airport express is used for music and is in client mode only. The only function the airport express service is to stream music from my iTunes to my home audio receiver.
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Is the bonjour service something I need? How hard is it to disable?
Bonjour is problematic. More in the latest devices with Yosemite and iOS >8
My Airport Express keeps causing IP conflicts.
Can you post the actual details for how the express is setup..
I am not sure how the Express can cause the trouble.. but lets start with exactly what it does in the network.
You stated.
The airport express is used for music and is in client mode only.
Please open the airport utility on a computer.. click on the express so it shows its configuration.. and post that as screenshot.
(I don't have express.. but this is what I want to see).
You can also click the edit and give me just the relevant bit of the wireless page and network page.. although most of it is right there on this screen.
Should I disable the bonjour sleep proxy? If so, where?
The answer to this is most likely yes.. the problem is where.. because I am not sure it is so easy as turning it off.
About Wake on Demand and Bonjour Sleep Proxy - Apple Support
There is stuff everywhere about it.. but not a lot about what to do when you have issues..
I can see you have multiple Apple TV.. they as well as the Express are possible sources of the problem.. if you turn it off in one.. can you turn it off in all of them.. I don't think so.. !!
It is better to simply make it stay put.. and make sure as much as possible it doesn't get involved in DHCP.. since your setup is such that you cannot really move dhcp to the apple router as I first proposed.
I don't think you have a problem with the modem.. which is problematic with apple routers.. because you do not have apple router involved.
I would still prefer to work out an arrangement where something apple took over as dhcp server.. even if it doesn't route.. and to do that, I think I would like you to grab a airport extreme.. a gen 4 or gen5 would be more than good enough.. you don't need to use it for wireless.. that is taken care of by the ubiquiti WAPs.. you just need some device from apple to take over the dhcp duties.. that will btw not stop the Meraki security device working on routing, QoS, firewall and all the other stuff it does. I just want something else to handle dhcp to the apple clients.