Okay here's what I'm noticing.
You don't recognize the advantage gained by pushing someone to the edge as that. You've reached the understanding that having center-stage is good -- and it is -- but you're mostly looking at the defensive benefits of it. In the second question the very first thing you've pointed out is that platforms help his recovery. Cool, but that's not really creating a good situation where you have positional advantage so much as it mitigating the disadvantage incurred from a bad one.
So let's break Falco down a bit. Risk-reward and let's talk about how we can work a better offense.
So the first thing that usually comes to mind for me is...
Grabs. You could get a lot of utility out of grabs as a positional tool. Your lasers force people to shield, take stun, or jump in order to manage them. This creates opportunities for free hits. Throwing people above you often forces them to move to the side to avoid a follow up. The fun part is that it doesn't even work all the time because Falco's throws are pretty solid despite what people will tell you. Throwing people off the level once they've been backed up against the wall is also solid. You can lead into grab with shine (shine --> JC grab is a really strong tool), or off your laser, and you can even dash dance into it.
One of the most useful utilities of grabs is simply how much they open an opponent up. While it's true that aerial-shine chains are safer vs a shield than most things, the opponent still has a lot of options during an aerial-shine sequence and you are playing one of the most fragile characters in the game. In a lot of ways you want to limit how many outcomes are possible from a combat exchange -- especially if you're likely to be shield grabbed and killed if the opponent does something good. I don't want to give the impression that aerial-shine sequences are utterly useless because they're not by any means. But you're trying to start a combo or get a hit when you're shield pressuring. Grab does that. The same shine you'd use to extend the pressure sequence with an aerial can also lead into grab. Hell, that shine can lead to another shine. The mixup potential is endless.
Shines. Shines are another reason why pushing people towards the edge or into holding the edge is good for you. Your shine requires people to DI sharply from you in order to prevent you from being able to follow. But at the edge that means they're going offstage. This holds true for many of your combo starters. If they don't DI away, you can dunk them. If they do, you can wall them out with bairs (and whatever else looks good).
Lasers. Once you have someone pinned (especially if you've forced them into grabbing the edge) they really don't have many recovery options because you can stuff most of their options off the ledge with lasers. This forces them to attack early or take a defensive role in order to fight their way back to you. Which you can play to exploit. If they're turtling, your biggest strength is your ability to harrass without really committing much -- things like moving in a bit with a laser to put pressure on them and then dash dancing to get out of the way of their shield grab or attack out of shield can be a great way to open someone up at the edge without really committing to much. It conditions them into waiting longer or attacking right away to break this. The former is beaten by simply doing exactly what you're doing or by using a variety of careful, low-commitment openers (laser --> shine, laser --> grab, laser --> shine --> JC grab, etc) to apply pressure and get them off the level. The latter is beaten by simply watching for how they're going to attack you and punishing it -- it's a more risky strategy on their end because they're trying to hit you. Bair is usually good vs that, as is dash dance grab, u-tilt, and walking away.
Falco actually has a really good ground game between those three moves, his dash dance, and his long dash SH distance. I notice you're focusing mainly on his aerials themselves and how you can play them in different ways but the core of most characters starts with the ground because it offers you your grab, your shield, your main movement options, and it's where most of the fighting occurs. If you want a strong positioning game, think about how you can sweep people off their feet while keeping yours planted. Grabs, shines, dash dancing, and SHLs are the best place place to start with that. Falco is all about control.
