Have you considered a four sector solution at each tower. This way you can deploy ABAB (e.g. 5800, 5775, 5800, 5775) where for four sectors you use a maximum of 45 MHz of spectrum.
When sectors on a tower are 180 degrees opposite each other, then you can use the same frequency. When sectors are next to each other, you need 5 MHz of guard band between them.
When the sectors are opposite each other, please make sure your sector antennas have a front-to-back ratio of 30-35 dB so that they do not cause self interference between them. For example an SM can hear the intended AP at say -60 dBm, and the AP behind it will be heard at -90 to -95 dBm because of the front-to-back ratio. This allows you to get MCS15. If you use sector antennas with less front-to-back ratio, then the SMs will hear the radios at a higher level (e.g. -85 dBm in this example if the front-to-back ratio is 25 dB) and cannot do MCS15 reliably.
With a three sector tower you would need to have 70 MHz of spectrum (e.g. 5775, 5800, 5825). Neighboring sectors cannot get the 30-35 dBm of front-to-back isolation because SMs on the edge between sectors will see both sectors equally well so the APs cannot be the same frequency.
So in this case more sectors on the tower is better and will also give you better SM density.
Even three sector solutions are better than the competitors, because competitors require greater guard band for their non-synchonized radios to protect against interference.
Synchronization applies between towers so you can reuse frequencies on different towers.
It depends on channels you will select for your deployment.
In case you will use ABCD Frequency assigment you will need 20MHz+5MHz+20Mhz+5MHz+20MHz+5MHz+20MHz=95MHz of spectrum resource for setup of 4 non-Sync APs with 20MHz channel Bandwidth per AP deployment.
In case you will use ABAB solution you will need 45 MHz of spectrum resource.
ABAB Frequency Reuse will not work with non-Sync Radios because of Primary interference, DL and UL frames will be not synchronized and one AP will produce strong interference for opposite one.