I also built my own 3G range extender with an almost identical off-the-shelf $50 Yagi antenna at a country cottage (2.2 and 2.4GHz are close enough for an antenna to carry both), so I've spent a while pondering those kinds of scenarios.
But addressing your points directly, I would look for OpenWRT-compatible devices with external antenna ports and the ability to do both 2.4 and 5GHz - and most likely try to use 2.4 for long-distance point-to-point links with Yagi antennas.
Hitting the bitrates you mention seems perfectly doable, although I must point out that the antennas are conspicuous (about the length of two Pringles cans). The challenge I found is having router hardware that can pin SSIDs to separate radios, because most of the modern stuff aims for diversity and prioritizes throughput.