Normally, setting all of the main speakers to "large" does not shut off the subwoofer, but it does direct the bass of the main channels to the main speakers only, so that only the bass from the ".1" channel goes to the subwoofer. Some receivers allow sending the bass to both the subwoofer and the main speakers, and that might be the "best" option if one wants extra bass, but it is pretty much never going to give a proper flat bass response that way.
Without knowing more about your current receiver, it is hard to advise you regarding it. In most cases, if one wants an improvement in sound, one should either buy better speakers or improve the acoustics of the room (or both). From what you say, there is a good chance you could improve the sound with a new receiver, but it is very likely that, at low volume levels, there will be minimal or no improvement in the sound. Those 10% THD ratings of which you speak are at the rated power, not at lower power levels. Even with your receiver, most of the distortion will probably come from the speakers (they don't normally give you distortion figures for speakers, because they are so bad that people would be shocked by them).
If you provided a link to download the manual for your particular receiver, I would probably be willing to look at it and give you advice about it in particular. Probably, getting a good subwoofer would be a better investment than replacing the receiver, if sound quality is paramount.
Also, you have not yet said, did you replace all of the main speakers, or just some of them (like just the right and left front)? If you have not yet replaced the other speakers (especially the center front), you would probably be better off doing that before replacing the receiver.
Really, your receiver would have to be an amazingly bad thing to be worse than tolerable speakers, assuming that you are using the receiver within its design parameters (i.e., with appropriate impedance speakers, keeping the power below [in your case] rated output).