I think having the extra ki points granted by monk are better than superiority dice in all situations. Superiority dice cannot grant extra attacks or stun an opponent.
I would go directly to monk 5 for stunning fist. I would not pass GO and I would not collect 200 dollars.
Next level I am sacrificing 1 Ki per short rest for (fighting style, 1/ short rest heal 1d10+1) so about even. Then the following level I am sacrificing 1 Ki point per short rest for (1/ action surge per short rest) - again about even. For level 8 (monk 5/ BM 3) I am sacrificing 1 Ki point for 4 superiority dice per short rest. Clear advantage to the MC build.
At 8th level, instead of rationing 8 Ki points over a short rest, you wind up rationing 5 ki points, 1 action surge, 1 second wind and 4 superiority dice. It's a pretty good trade off.
A [monk 5/ BM 3] armed with a Katana/ Jian [shortsword]:
Attack: 2 sword attacks [1d6+dex+2] plus 2 flurry attacks or 1 martial arts attack [1d6+dex]
Plus: Stunning fist, OHM flurry kncokback, precise strike/ disarming attack from BM, action surge, stunning fist.
A [monk 8]
Attack: Attack: 2 staff attacks [1d8+dex] plus 2 flurry attacks or 1 martial arts attack [1d6+dex]
Plus: Stunning fist, OHM flurry kncokback, stunning fist.
Note how in both cases, the damage is pretty middling. However the monk/ BM can: Move + attack twice + action surge attack twice + flurry for six attacks, spamming stunning fist, disarming strike, precise strike, OHM knockdown (and then use his free object interaction to pick up the stunned creatures disarmed weapon). You can also use action surge to take the run action (increasing your move speed), the dodge action (increase defence) the withdraw action (avoiding AOO to get to your priority target) then use your move to close the gap,
then attack + flurry for 4 attacks spamming stunning fist/ disarming strike/ OHM knockdown etc.
You gain an [action surge] plus flurry 6 attack + 4 sup dice + disarming/ tripping/ stunning nova option in your pocket for when needed. Its a totally worthwhile trade (although it does delay feats and proff in all saves)
Plus:
