Consider testing the emitter using a square wave centered at 0V and observe the transient response vs. using a square wave centered at Vpp/2.
Work on determining the max and min propagation times and how effective the method of checking whether or not the measured propagation time is within the boundaries is.
Experiment: tie a hardware interrupt to the Teensy so that when it crosses the high threshold, it sends a pin to HIGH, and when it crosses the low threshold, it sends a pin to LOW. Then, on the oscilloscope, observe how precise the threshold detector is (precise means consistently setting the pin to HIGH or LOW at the same received input amplitude).
Implement a voltage offset for our received signal so that the signal is centered at 3.3V/2 = 1.67V.
Design a multi-stage amplifier circuit attached to our receiver to amplify the signal so that the Vpk-pk is around 3V and has a band-pass response centered at the operating frequency. Need to find an amplifier with a slew rate of at least SR = 2*pi*f*Vamp = 2*pi*(41.67kHz)(1.5V) = 0.393 V/us.