Recent advances in micro- and nanofabrication techniques have led to corresponding improvement in the performance of optomechanical systems, which provide a promising avenue towards quantum-limited metrology and the study of quantum behavior in macroscopic mechanical objects. One major impediment to reaching the quantum regime is thermal excitation, which can be overcome for sufficiently high mechanical quality factor Q. Here, we propose a method for increasing the effective Q of a mechanical resonator by stiffening it via the optical spring effect exhibited by linear optomechanical systems, and show how the associated quantum radiation pressure noise can be evaded by sensing and feedback control. In a parameter regime that is attainable with current technology, this method allows for realistic quantum cavity optomechanics in a frequency band well below that which has been realized thus far.