How to determine irrelevant data in binary classification?
I agree that you could reasonably classify the stock that it relates to, and whether it concerns a trading intent or not, separately. Presumably, trading intent looks similar across stocks, so the two are not related much.

Your second and third ideas therefore sound relevant to me.

It's possible to consider a multi-task classifier too with deep learning architectures, one that tries to solve both at once. There might be small advantages to that, but it is more complex.