Honestly, as MK you can probably work around Luma as opposed to always dealing with them head on. Rosa/Luma can't really pressure you from range without taking time to send Luma out so you can effectively bait them to come a little closer and get some breathing room and time to think about options as opposed to letting yourself get pressured by trying to push back in a stationary position. I noticed that a lot of the time you could have stepped away a little and forced extra movement out of Rosa or Luma to reach you, giving you a little more time to act, but instead spent a lot of time in shield or attacking, trying to brute force your way through the Luma wall, and that's not really the kind of character MK is in my experience.
It's always good to remember that MK has great movement options that can pressure just as equally as his attacks can - above average speed, multiple jumps, dimensional cape - but his attack options are actually kind of linear if you want the most out of them since Dash and Grabs are your B&B, but are pretty predictable. If your opponent can clank with Dash over and over, or punish Grabs, it's just what they're gonna do and you absolutely need to make a different move, even if it seems worse.
Though, if you can't get around your opponent with movement, I figure there's a few attack mix-ups for MK that aren't so bad because they very quickly put Rosa at a disadvantage by disposing of Luma or otherwise just putting them in the free-fall state:
Drill seems to be pretty good for removing Luma, thus giving you an easier time with your more linear options like Dash and Grab. Even if you get punished, that small time without Luma might just be worth it. The particularly good thing about this option is that there are a few ways to mix it up to make it harder to punish, and it's actually pretty difficult to do anything about other than shield once it's in motion. Luma absolutely cannot block - which makes this perfect for getting rid of the pest and applying a little pressure to Rosa, too. Though you will likely get punished by a good Rosa, so use this sparingly.
Some of your regular moves are actually pretty good at just pushing Luma back, too. Jab, F-Tilt and F-Air are all pretty safe, fast options for just getting Luma off you so you can focus on the real threat for a while, though as with Dash, they can still clank so keep that in mind. F-Air has the benefit of not clanking, though you might just trade with Luma because of it instead - it actually feels like the least useful of the three because of this, though I could be wrong since Galaxia (MK's sword) has a decent disjoint. D-Smash is also a fast option for knocking back Luma, but because it's pretty punishable and hits low (May whiff Luma.) it's not ideal to use, though I would keep it in mind, just in case. Same goes for N-Air, though it does need to be be a clean hit to be of any real use (No late-boxes.), so it's kind of slow and requires some precision - again, not ideal.
Dimensional Cape is a huge deal IMO. Not only does it give you a few tools to get around Luma with one move, but that also gives it a great mix-up factor. Just like Drill, even if you decide to attack with Down-B and get punished, it might be worth it just because you've gotten rid of the Luma wall for a while - you might even decide to just go right for Rosa, which is an equally good strategy if you hit, though it's worth noting that Luma can't dodge a well placed Down-B attack (Which also has a pretty obnoxious range on it.), so you should prioritize them instead if only for consistency. If you don't want to attack with it, which is a viable option, you can likely threaten to get in their face with an autocancel Cape, forcing them to try and punish a pretty unpredictable movement which you can easily just fake-out and stay in place with. Of course, it still requires smart use, but it's one of my favourite movement tools for a reason.
I'm not an expert on the Rosa/MK MU or anything, but I hope some of this helps or at least gives you a few ideas of your own on how to deal with Luma as MK. My main advice would still be to use more movement as you seemed to be pretty scared of being above Rosa, which, while understandable may mean you end up with skewed priorities. Being walled out forever is no better than having to deal with U-Airs that might not even KO, and correct use of options like Dimensional Cape or retreating to stage platforms might just make it so that Luma is a whole deal easier than a head-on assault...
