Speaking for myself, it worked exactly how it was intended, I even died once right at the beginning and won the next try like I saw you mentioning in the comments to someone as the "ideal" playthrough experience. The ending definitely made me work hard after I was just cruising ahahah.
Ye, these games seem to always end up struggling with this kind of thing and to be fair, it's understandable, it's a difficult thing to know how to fix but something that is also easily noticeable. I guess panning could help (I don't know if there's any already or not as I didn't play with headphones) but only for headphones so the only other thing I can think of is to try to make the sounds for each thing be on a different range of frequency, like, the horizontal lasers could be a low tone, the green shooting middle and missiles more high pitched. Basically, you'd first focus on making it so that all the sounds playing at once in the most messy way would still sound harmonious rather than choosing a sound for each and then try to make it work together.
Another idea could be having slightly different rhythms for each thing so the chance of them playing at the same time is lower. Then, even if it's still a bit messy it's not as constant which might be better. For rhythms I mean you could have something firing on slow septuplets and something else that also needs to be just as slow could be on a slow sextuplet. The septuplets are a bit faster but it's a minimal difference that I think would keep the mechanics of everything still balanced and by having a rhythm everything is a bit more harmonious, hopefully. But those are just some suggestions ^^
As for mixing, it can be hard, take your time and if you can get someone who already knows something about it to help you.
My Pleasure!