Asymmetric chess-like game with three factions – best approach for training AI?

I am training AI players for a chess-like game which has 3 distinct factions (i.e. different piece sets) and is played on a 9×9 board. The three factions are called Axiom (A), Blades (B), and Clockwork (C).

With help from ChatGPT, I have managed to create 6 different AI models, one for each match up (AvA, AvB, AvC, BvB, BvC and CvC), under an Alpha Zero style approach. The structure used (which I broadly understand but largely relied on AI for designing and implementing) is as follows:

“The neural network uses a compact 7‑layer CNN backbone that preserves the 9×9 grid: a 3×3 stem expands 22 input planes to 64 channels, followed by six 3×3 convolutions at 64→64 to build board features before the policy and value heads.”

After three rounds of training (with approx 600 games each round, before mirroring), I have decent AI players – e.g. I can win against the best deployment version around 30% of the time, and I am about 1200-rated at standard chess. But the playing level seems to be plateauing, e.g. when I deploy the latest version against earlier versions I am not seeing obvious improvements. My value head is also still tied to winning material rather than the final game outcome (if I set the value based on predicted win, the play falls apart).

So I have a few questions for this community:

1) Is my ONNX too small, and how can I tell if so?

2) When / how can I move to the next level and have a proper value head that predicts the game outcome?

3) I’ve just been doing the training on my Mac Mini, running games overnight. If I am not in a hurry, is there the need to rent a cloud computer to get further gains?

4) If I use my game logs across all 6 match-ups to train one mega-model, would this result in a stronger or weaker player than my existing ones? I presume it would be weaker (due to less specificity), but ChatGPT says it can go either way, because more data may lead to better patterns. If I switch to a mega-model, do I do it now or later?

I appreciate the training here is more complicated than for standard chess, due to the bigger board and numerous match-ups. So I’m not aiming for an advanced engine here, but having strong AI players (equivalent to 1800 rating would be great) will help me with balancing the three factions better. With a more advanced AI I can also use it to deduce piece values (e.g. by removing pieces from both sides whilst retaining broad parity).

Many thanks in advance!