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I decided to swap colors for the second 200 games, to immediately average out any color bias or first-move advantage. (I am not sure there would be much of a first-move advantage in these tests, as Fairy-Max randomize its first three moves, so the chances that it will play a pretty useless first move are appreciable.) After 116 games they were exactly equal. I see a similar draw rate as you.

So it seems the following tentative conclusion is justified:
The setup with G=R+K and W=B+N is very well balanced, with 20% draw rate.

I have been watching the games for some time, and they are very
interesting. All pieces participate actively, their values are such that
there is plenty of opportunity for nearly equal trading or light
sacrificing. Most games get into an end-game, and because of the unequal
material, the end-games are always fascinating. It is half familiar because
of the Persian army, half exotic, (but not weird). All pieces are highly
symmetric, normal Chess pieces.

I really think this is a wonderful design, and to my taste it is immensely
aestethically pleasing. SO TO ALL READERS: I can highly recommend it!

I will continue to run tests for more exact piece-value determination, to
better tune Fairy-Max.