You could connect 2 loadcells to one HX711 so you would only need 18 HX711s. You can also clock them at a slower data rate like 10kHz so working with long wires may not be a problem.
The amount of current required by each HX711 with one laod cell is roughly 5V/Loadcell resistance. So for a 350 ohm cell the current is 5/350 ~ 14.3mA. Depending on how you wire the grid, AWG 20 for power and ground could be OK