Full hops are a high commitment option that are predictable and easy to react to. Falcon generally doesn't full hop unless it's for movement or comboing. What you really want to do against Falco is use platforms to your advantage. Watch any good Falcon against a Falco and you'll see them flying around platforms around lasers. A waveland off of a platform affords Falcon multiple options while still avoiding lasers. If Falco is advancing with a laser, you can jump over it, waveland off, and knee the bird in the face. If he chases you onto the platforms, you can shield, shield drop uair him or just shield drop and reset to neutral. Basically, it's better than getting lasered. You can also practice powershielding (While dash dancing! Very important) against a level 1 CPU by staying far enough away, but it's slow going, and pretty tough to do in a match.
Raptor boost is pretty bad to use unless you're using it as a mixup, tech chase, or some times to punish high lasers as it lowers your hitbox. It's slow to start up, slow to move, and inconsistent in hitting the person after it triggers. If you keep doing it under lasers, the Falco can pick up on that and start shooting lower ones, so it can't be your only response. Often you can SHFFL a nair over lower and mid-level lasers, though, and it's something Falcos ***** about enough that you know it works.
You're on point with trying to keep pressure on once you're in. Even if you miss a tech chase, don't let him get away from you. Keep the DD pressure on, mindgames him into making a mistake out of a roll if you can't follow up, whatever. Just don't let him get away. He beats you in neutral because he never lets you get into neutral.