“I read before about theories that Europeans brought mosquitoes carrying a virulent strain of malaria to the Americas...”
~~~
Mosquitos have very short lifespans. Seems unlikely they could make the trans-atlantic trip, even if generations of them somehow managed to stay with the ships.
It seems more likely that the Europeans came as carriers of that strain of malaria and the native mosquitoes transmitted it.
Female mosquitoes can live up to a month. Male mosquitoes only a few days after breeding. Not out of reach for a transatlantic trip with good weather and winds. Not to mention the fact that the bilges of wooden ships were likely superb mosquito breeding ground.
I can see a female mosquito laying eggs in the bilgewater, with eggs and larva dumped at the end of voyage when the bilges were pumped out.