Optimally convert (small) boolean expressions into NOR form by hand
I question the real value of your question, since noone ever has only simple NOR gates to work with in practice. There are algorithms for finding near-optimal minimised solutions to less trivial expressions. https://en.m.wikipedia.org/wiki/Espresso_heuristic_logic_minimizer

Brute force is the best approach for a small problem, I fear.