Yeah, Fox grabbing Luigi doesn't mean much. Hence shield keeps him alive so long aside from gimp kills. Those are scary though.
I know very well that you know very well what you're talking about and that you're a great player, don't worry about that. Either way, I take everything under consideration no matter who it comes from. You're no exception.
That being said, there aren't many 'great' players that have put the time in to playing Luigi well. Ka may be one of, if not the only one to do so to date. I'll confidently assume that you're a better player than any other 'good' Luigi players you've played if you're 4 stocking them. That should never happen unless you are a better player. I'm sure you understand this.
At the same time, Eric is a 'great' player, so is Ka. I'm not a great player. I live 6 hours from the nearest 'great' player and rarely play at all. Yet last time I played Eric in tournament, which was only a few weeks ago, I used Luigi in the second match of our set. It came down to each of us with over 100% last stock (he Bair'd me ftw too

).
There is no reason for a 'great' player who knows Luigi that well to struggle with a Luigi like me so much. The other Falco I played that tourney was Tim, in crew battles we went even in stocks but I nearly took 3 with my 2. He has plenty of Ka practice too.
This is generally what I gather my perspective on Falco vs Luigi from. When I played Ka, Falco and Luigi are characters I've yet to use, so I don't know what it's like from that side. And I haven't ever played a Luigi from that side of the match up.
I use Falco as well, and would like to know how to play the match up, but from the Luigi side, I can tell you what I find works against me and what doesn't. So far things that have been pointed out as 'working' aren't things that have worked on me, and from what I've witnessed, they don't work on Ka either, for good reason. (he's better than me lol)
1 is early kills. Whenever a Falco can get that combo into Bair or Dair for a good edgeguard before 100%, that can get him the needed lead. That's essentially the basis of what I'm trying to avoid on stage. It's not the lasers or approach or spaced Bairs, it's the combo to the edge into one.
Bairs and straight attacks are easy to avoid, or simply shield. Trading hits is also in Luigi's favor (for the most part). When it comes to higher %, every one of Falcos attempts to kill can be avoided if he can't combo into it (or if Luigi gets stuck on a platform)
That's something that works. Lasers work for getting more potential opportunities to set that up, but that's only a potential and can be avoided. A 'good' Luigi should be able to, or at least will learn how with enough practice. A 'great' Luigi will very rarely let that happen, if ever.
That's just something I find to be CONCRETE in this match up. Not laser game. Early kills is where the game changers come from, and that comes from the better player, not the overwhelming lasers or bair spacing. :\
That's my input to this match up.