The way I use fair and bair is by throwing it out more as a defensive. The hitbox is there to keep them out and give me space. That's the gorgeous thing about Peach - if she was given the time to place that hit on your shield, she's gotten in too close and she's safe then to either retreat or follow up.
Peach loses when she's either kept out via zoning (Marth fair), beaten in speed (Rob fair), or when her advantage on shield is taken away (MK Upb). Of course there are answers to all of these.
Throwing out fair and bair
hoping they mess up sounds like the worst plan ever.
More effective would be
knowing, or at least making an attempt at
predicting what they'll be doing, and throwing those moves out as an answer.
The shield thing doesn't sound very effective. Against knowledgeable players, floating above a shield is highly punishable and it's one of the last places I want to be. Certain characters apparently have this
gaping vulnerability there though, like Toon Link. From there you can do silly things like tech chasing the shield options like you said.