Thank you everyone!!
And my apologies about the confusing thread - I decided it would be better to break out my question about 3.3v HC-SR04's into a separate thread, but it appears a mod disagreed with me 
I will see if I can get my hands on some of the HC-SR04P's. Sounds very promising!!
Also, last question for anyone still reading: if I'm using a 3.7v LiPO to power my ESP8266 and my HC-SR04P, I'll at least need a linear voltage regulator to drop it down to a safe voltage, right? Something akin to this?