Requesting help with setting up dorm wifi for large number of users and unique constraints (wireless backhaul & limited channels)

I have received the go ahead for setting up commercial wifi for my dorm to use. Dorm management is restricting us on the specifics of the set up due to contracts with Boingo Wireless and with their construction regulations.

Here are the specific restrictions and details on the set up:

• Only channel 11 for 2.4ghz and channels 161 and 165 may be used.
  • Will this affect the usefulness of MU-MIMO and Tri Band routers? I'm assuming MU-MIMO will work fine but I am not sure about Tri Band.
• We will have about 80 users (+/- 10), all college students so there will be a lot of bandwidth used.
• No exposed wire or ethernet cables may be used (other than modem to router) - all users will be using wifi.
• We are getting a Gigabit Xfinity plan
• Budget of $1000 for equipment (could do $1200 if worthwhile)

The current plan is to use 3 routers (+modem) to provide coverage in 3 hallways. The dorm is a T shape with the modem+router in the center of vertical line of the T. The other two routers will work as secondary access points on the top left and right corners of the T. We intend to use the 2.4hz freq to backhaul to the central router (because we can't use ethernet cables to connect them) because I believe it will have greater range and penetration - we are getting gigabit so I believe it does not require 5ghz especially if we can split it between the three routers. We could then use 5ghz channel or channels (if triband) to connect to each device. I currently am looking at Netgear Docsis 3.1 Modem and the ASUS AC2900 or the Netgear AC5300 for routers.

So, does this sound reasonable? What routers would you recommend for this project? Any changes I should do within the constraints (maybe more, cheaper, routers)? Is a wifi backhaul possible with consumer routers? Thank you for any help!