Carpet and rugs are useless for absorbing bass.
To reduce the boom on the cheep, the only solution would be to experiment with sub placement. Something that will help with that is test tones, as they will tell you what frequencies are the problem.
These may be useful in that regard, I have not used them myself, as I just found them a few minutes ago looking for cheep tones with the resolution needed; they appear to be correct (I ran a few of the previews through an RTA), and it would only cost about $14 to download 30-100Hz.