It doesn't have to be a slim profile turntable like a B&O. Even a Technics SL12x0 is under 7", so I'd think that any turntable without a Herculean-sized plinth and suspension system would fit.
For example, the Clearaudio Performance CMB Turntable w/ Satisfy Carbon Tonearm is right in your budget range and is 5.1" high.
For example, the Clearaudio Performance CMB Turntable w/ Satisfy Carbon Tonearm is right in your budget range and is 5.1" high.