You're correct, the 36x are not compatible with 6.4, so you will need to stay within the 27x range.
The issue with the higher gain antennas are:
a) They are not FCC approved for our hardware. FCC requires products to be approved 'as a system', so we test and submit all our antennas with all our APs, but no other 3rd party antennas. Cisco and all other WLAN vendors are the same.
b) At 34dB, that means the AP *could* exceed the max EIRP in some bands (if the AP power is set to even 2dB) and *absolutely will* in other bands (even if the radio is set to 0dB/1mW).
c) 34dB antennas have beamwidths on the order of 5-6deg, which is increbily narrow and unnecessary at these ranges. The high gain antenna will result in a large amount of RF overdriving the receiver and causing a decrease in performance.
Anything under 1km will work with a 60deg to 30deg antenna (we do 30Mbps at 7mi and 70Mbps at 4mi with the 30deg antenna on a 274).
Two APs in the middle will ensure maximum thorughput and the most efficient datapath (esp if the intent is for voice). With only one AP in the middle, you will have to deal with a multi-hop mesh which will double the latency and cut the throughput in half, but you will also need to set an RTS/CTS threshold to avoid hidden node issues between the two far endpoints, which will decrease performance and add a slight bit more latency to the path. With four APs and two distinct and separate point to points running on separate channels, the datapath is linear and not impacted by the hop (impact is approx 1-2ms).
See attached for a quick and dirty graphic that is exactly what you are looking at. And four AP-277s will be THE most efficient topology, as you won't have to worry about mounting APs and antennas or weatherization or antenna cables, just mount, point, and shoot.
You can also use something like these two products to provide power and interlink between the two mid-point APs on the pole, with an outdoor industrial rated multiport POE injector.
https://www.microsemi.com/products/poe-systems/pd-9002gho
https://www.microsemi.com/products/poe-systems/outdoor-poe-switch