If you have that kind of budget, don't buy any CD player at all. A good DAC with destroy the same priced CD player and those at 5X their cost, period. Stop spinning CDs. Moving parts, jitter, optics, laser, motor, etc.
Buy a simple program like dBPoweramp or similar, rip all your CDs in at at least 24/96k FLAC or WAV and prepare to lose your mind when you hear them through the right DAC.
My Eastern Electric tube DAC ($1,350 new), a Line Magnetic tube DAC or used DAC from Chord, Mytek, Ayre, Auralic, etc.