I setup the AirPort Extreme with DHCP/NAT as the main router and then added three 3rd gen Airport Expresses all on bridge mode. Only problem I had was getting the 3rd express to pull an IP off the LAN port of the extreme.
Is it really the main router though or is the cable modem actually the main router and you are doing double NAT??
What you said here..
I had to plug it directly onto the cable modem LAN PORT.
is impossible if the cable modem is bridged..
There is no limit to the number of addresses you can assign lan clients.. 50 is the wireless limit.. 199 is the limit the airport sets via dhcp range for all clients.. but that is able to be changed to 254 of which you should never attain in the real world.
However what you are saying is not unusual.. people seem to often hit this limit.. 2 is enough.. at least of express and the third is the odd man out..
I have no idea why it should be so.. as a test plug one of the express into another express.. does it work ok then.. ??
Did you make them all completely different names. Remember you cannot duplicate names on a network. Setup the third express in network isolation then plug it in and see what happens.. Any screenshot you can show me of the problem can help..
If you happen to have a switch available.. can you please try that.. so you have extreme--switch---expresses.. so all the express connect via one ethernet port on the extreme.. that will work perfectly fine since extreme is gigabit and express are 10/100.. so use a gigabit switch.
ALso is there a way I can control the guest network on all 4 devices ( 1 extreme and 3 expresses) using just the extreme? Meaning can I configure the extreme for guest network and it activates across all the expresses via my LAN?
Guest across multiple express will all only work if the extreme is setup in full router mode.. and you are using guest on express that is therefore controlled by the extreme.. that is how it always works.. shut off guest in the extreme and guest will fail on all the express units.
AirPort base stations: About the Guest network feature - Apple Support
BUT.. some ugly sin in camp of the Israelites..
The airport guest wireless is SLOW .. like I don't mean SLOW.. I mean 40 years crawling around the wilderness with poisonous snakes.. and earth opening pits before you get to the promised land.
Google slow guest airport wireless.
See http://rkuo.com/2014/09/02/airport-extreme-bugs-and-guest-network-performance-pr oblems/
There is no solution.. it is just badly engineered.
This guy is VMWare engineer..
http://www.chriscolotti.us/technology/apple-airports-dirty-little-secret/
Dirty little secret.. Indeed.
If you had asked before buying I would have said buy Ubiquiti wireless products. Apple are purely domestic. Ubiquiti is almost the same price. And is much closer to pro level. No silly the third unit won't install.. proper wireless management tools.