Airflow through a trombone is not greatly different - sometimes it's less - than through a whistle. The reason it takes a hell of a lot more pressure to play a trombone is that the air has to be forced through closed lips, to set up a vibration. With a whistle the lips present no obstruction at all. The techniques are so fundamentally different that adjusting between them is quite easy. I'd be surprised if this is the problem.

I'd be more inclined to do another spring-cleaning of the whistle's innards in case accumulated gunge is still lurking. (I assume care is being taken to ensure that holes that are supposed to be fully covered are indeed fully covered. If not, you would certainly be at risk of the distortions described.)