I am not sure how to improve this situation.Easy: new speakers. Your bookshelf speakers are max'd out.
Your amp has tone controls so what you might try short term is turn the bass down. Your little speakers can't handle it. Then turn the sub up to compensate.
Its a crap solution but all there is without better speakers, since fundamentally your problem is nothing to do with the speakers its you. Play them within the range they are intended for, or buy ones designed to play within the range you want.