An alternate solution could be to simply merge 2 fields together into a rectangular shape as pictured below. If you rotate them, you can get them just as compact as before.
In total, you can fit 6 fields like this within the coverage of a Granary.
If you don’t rotate them like the layout below, you still get almost total Granary coverage. Only the protruding middle bits are not covered, and villagers generally stand in the middle of fields so it is near total coverage anyways. I’d even be in favour of increasing the Granary radius to fully cover the longest dimension and giving them a small cost. That would let you support 8 fields per Granary and make them more forgiving to use for hunting.
For placing these fields, you could either hold shift and scroll to rotate, or have two options for the different orientations in the build menu. Africans have lots of empty slots available so it isn’t much of an issue. The different orientations could also have different default resources when built (but once built could be toggled to the other resource). These fields could even be separately selectable so you could more easily select and toggle only a portion of your fields at a time.
Example of build grid:
→
The new grid is also a lot more consistent with the default European layout.
European buildings for comparison:
Overall build time could be 20 seconds like every other agricultural building. Cost could be increased to 150 wood to make it more comparable to other buildings like Mills or Estates.
It is also really strange why fields are not buildable in age 1. Is this to idiot-proof the game against AoE2 players?