I hope it is a fun experiment. Thinking about it in my head though, I suspect you are over-estimating the LFO waveform's ability to be heard. To my mind there is very little difference between sine and triangle wave in an LFO. Square wave? Sure, it makes the sound on/off.
Two of my favorite albums are Jeff Beck's Wired and BLow By Blow. The two records sound similar and were my go-to LPs for turntable testing. BUT... the electric piano on them was hard panned left and right and the trem was like a switch. The piano sound ping ponged left and right all the time. Not a smooth slide left to right and back, but a hard switch. Listen to either channel alone and the piano turned off and on a couple times a second. VERY annoying.
I think your LFO would have to control an interface that was totally electronic. meaning no bulbs and no photocells. A bulb is not instant on or off. An LED pretty much is, but not a light bulb. SO any sharp turns on your LFO curve will be smoothed out by a bulb's inherent delay. Likewise, photocells are not instant, they take some amount of time to recover each pulse. So there again, they tend to smooth out any sudden jerks in the LFO wave.
Sine and triangle waves tend to be smooth. A sawtooth wave tends to be a little more precussive.
I could be wrong, but I think the differences between your fancy waveforms would be like switching cathode resistors on your input stage between 1400, 1500, and 1600 ohms. In other words, not a lot.;