Well, if you connect the UFO output to a small speaker, it would output a constant 75Hz buzz (square wave with lots of harmonics). However, it has no relation to platter speed. What is needed is a differential between a reference tone and one generated by the platter. Hence you get interference beat patterns. Basically the audible version of a visual strobe.
So I can't think of a way to make the UFO useful for you. What might work is if you run the system backwards. Rather than illuminate the strobe, have the strobe optically illuminate a sensor. This optical encoder can then spit out a tone that is proportional to platter speed. It can also be compared to a reference (multiplied) to create an interference tone. I suppose you could make it operate like a metal detector. Lowest tone, or perhaps a null tone, means proper speed.
A cheaper method would be to get a calibrated tuning fork and an LP with a reference tone. Pain in the butt, but it would be very accurate.
So let me ask, I am going to assume your sense of pitch is highly refined. Do you find a slight error in TT pitch really annoying? I'm curious if you think it bothers you more than average. Do you feel you have to adjust for each LP? I'm wondering if the standard visual strobe is inadequate. You have me thinking here, that maybe there is a need for a platter speed sensor that is 100x more sensitive than what is available. Maybe something that can even detect the slight cogging from a dc motor.
jh