How to make the output of a ring oscillator look more like a rectangular wave?
If you want to preserve the phaseshifts of each stage, then load EACH stage with the identical and additional tap-off circuit.
Avoid positive feedback in the first stage of the tap-off circuit, because any snappy/abrupt edges will inject charges onto the RingOscillator capacitors.
Have that tap-off be an over-driven differential stage, with no feedback. Then the downstream circuit in each tap-off can be a positive-feedback circuit to provide the 50 picosecond edges you want.
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regarding need for square edges: 10pF and 10picoSeconda at 3.3 volts will require

I = C * dV/dT = 10pF * 3.3v/10pS ==3.3 amps