So what is the output of your 'show ap mesh topology', specifically the mesh link SNR/RSSI? With the 802.11ac radios, esp with the 27x platforms, you can EASILY over-drive the radios (putting too much RF into the APs which essentially 'distorts' the quality of the signal'. If you are using AP-277s at 65m at max power, I could easily see the RSSI being too high and you needing to drop the Tx power on each side to improve backhaul throughput.
When you tested a wireless client, was the client on the 2.4Ghz or 5Ghz radio off the CAPs?
You have full gig/full all the way through, there's no 10/100 power injectors in the mix between point and portal, etc? I've seen a 10/100 injector on a gig rated switch result in a 10-half port negotiation and throughput under load was atrocious. Since your wired performance from the switch is solid, I don't think that would be it.
As far as APs on the far side of a mesh link, do you have any MTU-specific configs applied to any of your AP groups? Did you create a new AP group for the APs in the other building hanging of the mesh point? Because you are running the mesh in tunnel mode AND the APs are tunneling GRE to the controller, if you set any specific MTU on the mesh link or on the CAP group, you can hit an issue where packets are getting fragmented. If you have set smaller than default MTUs on your wired infrastructure between the two, that can cause issues as well. Something else to look in to. An easy way to test would be to take a dual ethernet port AP to the building off the point, wire the AP's ENET0 to the switch and let it come up as a CAP, and apply a tunneled wired profile to the ENET1 port and test throughput from a laptop. If you see the same poor performance, you know you have a dual-tunnel/MTU issue. If not, then you know you have an RF issue on the other side.
The other fix to remove MTU/dual tunnel issues would be to set the mesh link to bridge, but then you need to make sure you untag the proper native VLAN on each side and tag the proper VLANs for tagged backhaul on the uplink ports on the point and portal. If you decide to change it, DO NOT do it if the mesh link needs to be active as it will drop and if config isn't exact, will drop the other side, or test it in the lab before rolling out.
I've done plenty of CAPs behind a mesh point and have never seen a system performance issues like that unless it's an RF issue.