I think that temperature variation will kill it anyway unless you employ some very clever compensation techniques. You have minimum 10% variation in velocity with temperature and velocity is the main factor in any timing that you must use to measure distance. That temperature variation cannot be accounted for because it may go from 100 C at the head through a cold patch at (I guess) around 30C then back up to 60C as the signal approaches the bed. Once you had set the thing with a warm head and bed then the results would be way off with a cold head and bed so it would need setting for every different temperature you use and for every location on the bed as temperatures vary depending on where you are then once you have opened a door or walked round the room the air moves and your readings are wrong again.

You also have a small variation in the velocity depending on frequency so any frequency sweep method would need more compensation tables. If you use eg. 40 kHz then you have lambda of around 8mm. No way on earth can you distinguish how many wavelengths you are away without moving the bed up and down significant amounts and without knowing if the head will crash how can you know if you are one wavelength away or more.

I am watching with interest to see how you overcome some of these (and significant other) problems. I looked at doing this a couple of years ago as I have done significant design work in ultrasonic sensing, I abandoned the idea because the further in you go the more problems arise.