Is the Airport Extreme 802.11ac base station the ONLY router and WiFi base station in the house? I'm wondering if there is maybe multiple subnets in play.
Does your problem iMac network normally with the other iMac and with the internet? that is to say, do you have issues with just administrating the Airport Extreme 802.11ac from this iMac, or are there other networking issues happening?
Can you administer the Airport Extreme 802.11ac via an Ethernet cable to one of the 3 switched ports? Just an experiment to isolate WiFi connection vs Ethernet connection.
What happens if you give the iMac a DHCP Client ID (wild suggestion, and I do not really expect it to change anything). System Preferences -> Network -> Advanced -> TCP/IP -> DHCP Client ID (make it a simple upper/lowercase/number name). Again, I do not expect anything.
What happens if you clean up your System Preferences -> Network -> Advanced -> WiFi -> Preferred Networks list. Delete any entries that are not normally used. If there is more than 1 valid entry left, drag your Airport Extreme 802.11ac network name to the top of the list.
Does your iMac get a strong signal from the Airport Extreme 802.11ac. Spotlight -> Wireless Diagnostics. Via the menus find Utilities WiFi Scan and Performance.
For the WiFi Scan you want to make sure you are not getting interference from other WiFi base stations and 2.4GHz/5GHz signal sources. Also make sure there is not another WiFi base station using the same name as your Airport Extreme 802.11ac. RSSI in the -40's is great. -50's OK, -60's and that is acceptable if there is no interference. After that, it is just plain lousy. Noise should be -90's and maybe high -80's, but I would prefer not to see any -80's for Noise.
You want your 2.4GHz channel to be at least 5 channels away from any neighbor's WiFi base station as each 2.4GHz channel uses 5 channels of bandwidth. 1, 6, and 11 do not overlap and if possible choose one of these if 5 away from any neighbors. Of course if the neighbor is showing an RSSI of -80's or -90's on that channel, they are not really very strong signal, so if in a condo/apartment it is good enough.
Just in case this iMac also has normal connection issues, then I'm going to list other sources of interference (which may show up as Noise above). Other WiFi base stations, 2.4GHz cordless phones, 2.4GHz baby monitors (the worse as they never turn off), Microwave ovens, metal kitchen appliances, floors and walls (especially with metal studs or concrete with rebar), USB-3 devices with poor shielding or poorly shielded USB-3 cables (you could try disconnecting all USB devices for a test).
Toggling Bluetooth (as it uses 2.4GHz) or even delete the Bluetooth preferences. Usually not an issue, but often times they share an antenna.
Blowing away the WiFi preferences
/Library/Preferences/SystemConfiguration/com.apple.airport.preferences.plist
but this will mean setting up the System Preferences -> Network all from scratch (so maybe same a copy to be put back if you try this).