Or probably you're just not as deep into Brawl as this mod requires... To be fair, it was planned specifically for high-level players, by some high-level players and other Brawl analysts (and some Brawl die-hards).
BBrawl does preserve most of Brawl's core game, which means that its campy, spammy, defensive and patient style is all there; everything but chaingrabs, locks, and other silly abuses.
Another of BBrawl's goals was to "avoid uniformity", and mantaining every character as unique as possible, with strenghts (some characters are really safe or have long range, others punish with hard hits, or have heavy weights, etc) and weaknesses (some characters can't kill easily, others die too early, lack range, etc), changing as little as possible from their individual original designs.
As for the scenario you just planted, there are actually three ways to beat a Falcon Punch Approach: the two you just described (both are pretty risky, though), and a third one which is actually much easier: see it coming (it has a very huge start-up, enough to react easily), stay just away from the hitbox, and punish its cooldown (there is a large window to do so), which is actually the most effective way to do it.
Any Balanced Falcon player will be careful with their punches and will force opponents not to commit too hard, or at least not to be predictable. It's a tough lesson, and it hurts (I once got Punched for playing around with Nayru-Upsmash gimmicks), but that's actually how many things in Brawl are: you are too aggressive, you may get punished, That punish may be hard.
TL;DR - BBrawl was not made for fun matches.
That's its strongest and its weakest attribute, because while it was carefully crafted to be good for competition, it has little appeal...