The system you have is designed to play mainstream music at casual listening levels. It has pretty good fidelity for the price within those parameters!
However, with the type of music you want to play and the emphasis on low notes presented therein, you are simply exceeding the ability of the sub. There are probably other 8" subs that would do a much better job, but the one you have needs to be able to play cleanly up to the crossover to the tiny woofers of teh speakers (maybe 180Hz).
The bottom line is that being able to play low cle4anly is expensive.
It is disappointing that Edifier doesn't have some sort of limiter or bass filter such that those low note would not make it to the sub (rather than the sub crapping all over itself).
This unit clearly will not fit your needs.
You need to decide what is an appropriate compromise between:
1) Spending substantially more money for a system that will play these low notes without any struggle.
2) Keeping the budget around $300, but finding a system that will not attempt to play frequencies beyond its capability
The JBL LSR-306p's I recommended are an example of option two and the option suggested by nbk13nw that I quoted below is an example of a good compromise that probably cost somewhere in the $500-$650 range!
Tell us what you are thinking and try to listen to some other options and give us some feedback and we will help guide you. If you have access to audio stores that will let you listen to lots of options (bring
your music), we won't have a lot to offer!
Last, consider that a system like the JBL's that nbk and I mention are sold at Pro Audio stores (like Guitar Centers if their chain reaches your region). IME, the sales guys in Pro Audio are at least a little more knowledgeable about their products (often they are aspiring musicians who support their music habit with a day job, but they are interested in the gear and quality sound)!
A couple of questions:
What is your source for music? Computer? Phone? Radio? CD player or media server?
How big is the room and how close do you sit to the speakers?
I started my new computer build with some Edifier speakers and sub. I never played any bass boosted content but found the bottom end was lacking. I ended up with some JBL 305's and the matching 310 subwoofer. It sounds incredible nearfield. Raise the budget a bit and take your time if need be. You will not be disappointed.