If you really do want a bookshelf that will meet your needs, only one company can make a speaker that fits your description and the is the Audio Transducer company. ATC.
First you need a sealed alignment so that the woofer will not decouple from the box below tuning. A good sealed speaker will have a higher F3 than a vented one but it roll off 12 db and not 24 db per octave. So they have more low bass. If I make a small powerful speaker and I have, I always choose a sealed alignment.
Billy Woodman of ATC who is a transducer engineer by training makes his drivers in house to exacting specs and tolerances. His transducers have much lower distortion than the competition. His drivers have very linear travel. Above all he has mastered the art of cooling so his drivers don't burn out easily. He very very seldom gets a burnt out driver back for rebuild.
What you are seeking is the
ATC SCM 11 which is just in your budget range. I can assure you the drivers in this speaker are totally above and beyond anything else. This is absolutely the only speakers in the world that will meet your criteria within your budget.