03' 330i with the HK system and BlueBus. Recommended upgrades?

I never thought the system sounded bad, honestly, far from it even! However, there was always I felt a little bit of muddiness in the bass, despite those ancient 6x9 rear deck subs holding up just fine. For anyone with experience, firstly, how would you review the original HK system for these, and secondly, how would you go about upgrading them?

I've looked at the Bavsound kit, as I'd like to steer away from putting a new amp in for the time being, as I'm on a somewhat tight budget and I would likely have to do the speakers or amp one at a time, and of course the stock speakers aren't the greatest. Any recommendations for/against Bavsound, or alternatives? Number one rule I have though, absolutely no adding subs. I need the trunk space desperately, and I've never felt the need to absolutely crank it.

If you need any more information, please ask! Thanks in advance

Edit: Also forgot to mention the main... requirements, I guess? Primarily, at or below the price of the Bavsound kit, I'm keeping the original head unit since BlueBus makes up for the lesser sound quality, and minimal PITA if possible. I can do the install myself, I've done plenty of interior work on the car.