For the moment, a nonstandard nxn board suffices. Very obviously, with growing n the long-range pieces become stronger with respect to short range ones. (Also, other effects come in play, e.g. the Q can't regularly win against a R if n is large enough.) Does any research on assigning piece values on a nonstandard nxn board exist?
Here is one idea.
- Create an engine that can play on that nxn board.
- Expose the piece value as option for tuning.
- Conduct piece value optimization using optuna hyperparameter optimization framework or other framework. Typical example is the optuna game parameter tuner.
After some trials you will be able to get a decent piece values.