I originally had them as heavy infantry that had a multiplier like that but changed them to differentiate them from Wokou Pirates (otherwise the only meaningful difference would be their resistance type). Melee shock infantry are heavy cavalry equivalents which are a unit type that shouldn’t be getting anti-cav bonuses.
A different approach to making them perform better against Manchus would be to make their melee attack deal siege damage (just like Desert Raiders). That would let them perform much better against Manchus specifically (who have 40% melee resist) without breaking the counter system. They should probably be depicted with a torch if that’s the case.
Part of the solution for that would be a rework of their production buildings.