I also try to double shine as like my default but I'm wondering what do you do after the second shine? Usually I just straight up jump since I'm not confident I'll always get a grounded shine but I'm thinking that there's something better I can do.
It can vary, but the more comfortable you get with doing it, the more you can focus on reacting to what happened after the first shine. Once you can reliably hit/block confirm the first shine, you have some more leniency in what options you choose. If I see they shielded the first shine and didn't immediately buffer a roll, I tend to just assume the second shine will hit on shield, in which case it can be treated the same way your mixups are without double shine. If you can't double shine and hit someone's shield, chances are you're thinking of options like grab, fadeaway dair, or waveshine back/forward. These all pretty much work the same after the second shine (albeit with less frame advantage because you have to land from the airborne shine, but it's usually enough to get the options out just the same).
My worry about double shine as a default is while you are guaranteed pressure/damage if it works, I have to start wondering about how the meta will skew more toward shield DI'ing the shines away(and vs Marth and Sheik those are grabs I really don't want). Maybe people will just opt to buffer roll to cover double shine or shine grab which means I'd want to skew more toward double shine or single shine laser/WD on reaction then. I think double shine is awesome vs spacies though and should definitely be used more against them since shield DI grab isn't as much of an issue and shine oos is common for both characters.
I have been thinking of WD in place as well as WD back primarily out of shine, but I do worry because I know on my shine single WD back I get shield grabbed by Marth a high percentage of the time without even going for it often, which makes me think they're reacting to my WD. This means I wouldn't try at least WD back vs Marth but possibly also not Sheik(if they did the shield DI away maybe after one shine you'd be safe?). It's probably great vs spacies/puff/peach though. WD down I like too because they're often discouraged from acting due to second shine, which means they will react late to WD down lag and I can get shine out and hit them as they react. It's why people try to grab Westballz shines basically but out of grounded double shine you'd get more options and extensions to make this more feasible and much much harder/potentially impossible to react to. If they buffer roll away you might be able to catch it with this too, whereas WD back you obviously wouldn't get it.
Double shine will be a very high priority for me so I can sort out exactly how all of this, and the meta, work when it's time to get back to training.
Getting your shine shield DIed and grabbed can be annoying, but I feel like that adaptation is pretty far away from the current meta. If someone is consistently doing it, there's tons of counterplay available, but even without brainstorming the best ways to deal with it, I would probably just stop double shining and start shine grabbing/aerialing. The shield SDI on the first shine only beats a second shine and loses pretty hard to everything else. The spacing of your initial shine matters the most, but it's worth mentioning that angling the stick down and forward to advancing shine can help mitigate shield ASDI, which really forces them to be getting the SDI timing.
As far as buffering roll, there's two possibilities. If they roll after the first shine, I feel like I'm able to just react and SHL out of the second shine. It's more than sufficient for keeping on the pressure. If they roll after the second shine, it's sort of like what I described above where you basically just treat the situation as if you were a player who couldn't double shine at all. Obviously it sucks if someone rolls right as you go for a grab or aerial, but neither of those options have so much lag that you'll ever be worried after doing them, you'll just get slightly less favorable timing/positioning with your next laser (or w/e you do).
Maybe you can offer some insight into shine laser pressure. It's something I used to do relatively often, especially vs. the long wavedash characters, but WD OoS is very rare after double shine, and the risk reward never seems to be there for me when I do get the read on their movement and laser out of shine. Outside of the spacies, the laser often feels like it helps the opponent become actionable quicker if they roll OoS than they would have been if I had just chased them without a laser, and the advantage gained from getting a laser on WD OoS seems minimal vs. the characters that favor it (because they go far enough that the laser doesn't allow me to threaten with anything immediately).
I don't think it's even feasible to react to the shine, so Marth definitely isn't reacting to your wavedash. Marth players just love the risk reward on post-shine options, so they time their grab right after when you shine. Their shield grab loses to immediate aerials and grab, but they can DI aerials away without much worry, and their grab punish is so much more devastating than Falco's, they just do it, not unlike ICs and Sheik mains. A hard counter to that is delaying the shine by a few frames after landing in order to catch players that always respect the shine, but of course that comes with the risk of immediate shield grabs, which can be hard to judge. Perhaps delaying the shine after super deep aerials is more consistent than tight aerial-shine timings, but in either case it seems to be heavily character/player-dependent. Some players just fiend off those shield grabs (M2K, IC mains), while others seem to prefer working their way out of shield or taking the grab (Armada, Falcon mains).
WD through Marth is actually really safe assuming you can do it quickly enough (I forget the leniency, but it's definitely possible). His grab goes so far forward that as long as you shined close, you can get past it before his grab box comes out, and he doesn't have any good OoS moves to keep people off of him (even up-B would sourspot at that range I think). This would also help to chase WD back OoS with a nice juicy dair. I feel like you would have to read that to get there in time, but Marth's lack of backward hitboxes greatly limit his ability to punish this sort of read OoS anyway.
I'm excited to see you start implementing double shines not necessarily because you will be double shining people all over, but I think it will greatly enhance your shine grab game. I think at the end of the day, the meta will always settle around players opting to risk being hit by Falco's grab over shine or other attacks because it's less solid/devastating, but that's obviously something you've done a great job of utilizing in the past, so Falco's shield pressure meta moving to a point where you're getting more grabs and having less people escape is a good spot to be in.