If you can quest well enough and handle the enemies with 2 heroes and playing 1 ally per turn, then you can avoid most of the worst treacheries if under 35 threat. You actually welcome them as it usually is like a free round when you're only drawing 1 card per turn. Aragorn and Eowyn can handle the questing, you just need to slowly build out a board of allies before pushing to stage 2 where the Nazgul will be an issue. Having that extra hero rescued really only gains you 1 more resource which isn't worth the threat of the Nazgul right away.
Escape from Dol Guldur using Core set cards only (straight solo and 2-handed)
I've always made sure to take my time on stage one. No need rescuing the prisoner (yes, I know it is a response, not a forced) until you can take on the Nazgul.