That particular Mirage speaker I would consider a Lo-Fi to perhaps lower end Mid-Fi speaker. Imo, based on specifications it is a design incapable of delivering a HiFi experience. I strongly suggest you save up your money and move in an entirely different direction, i.e. a more traditional Bass/Mid/treble speaker versus a skinny tower with multiple tiny woofers and a cheap, light cabinet. It seems, based on your discussion, that you can hear the lack of quality, now you have to save up and discover much better. Don't be cheap; put more money into it, or else you will only trade one set of performance problems for another.
Many people wouldn't care about the sound quality; it seems you may be a budding audiophile. If so, congratulations! You are earning your credits by owning different gear and learning what better sound is, and how to get it. I suggest you go to a very different approach, a tried and true one, by seeking a wider, heavier three way tower speaker with perhaps the traditional three drivers, bass (no less than 12"), Midrange, and Treble.
You likely will be shocked at how radically different things will sound, especially in terms of cleanness, coherency and bass extension and dynamics. You really have not had good sound with these speakers relative to all the other options on the market. Simply because a speaker is a "bargain" does not make it sound anywhere near HiFi.
Many years ago I was a poor student audiophile and I was tempted by all such cheap speakers, thinking they were really close to HiFi sound. Wow, did I have a lot to learn! It takes a lot more money spent and a lot better design/higher quality to have a lot better sound. The larger number of drivers tempts many, but often it is a cover for poorer quality parts in drivers and cabinets, crossover, etc. and results in poorer sound. Those are just the facts of it, and I hope that you will move in a direction of more refinement over time, and find great satisfaction.
Your conclusion, "...maybe this is all they've got and I'm asking for too much from them," is correct. There is a world of better sound based on better design and build quality available to you. I have no axe to grind against Mirage; it matters not the badging on the speaker, I would assess it the same regardless of brand.
I hope I have not been too harsh, but until one knows for certainty that the speaker is the problem one will not move off of it, and could spend a lot of money hopelessly trying to get more out of it than it can provide. Imo moving to a passive preamp would be an utter waste with these speakers, and that comes from someone who has experience with fine passive preamps and owns a beautiful one. :)