FWIW I have had some success transmitting data at 1000 baud over short distances using 43kHz underwater transducers. I am using FSK and a software PLL running on an attiny44a to decode the received signal. The attiny is fast enough to run the software PLL code as long as the frequency is below about 60kHz. The transmitter uses a SI9986 H-bridge, which allows me to get double the drive voltage to the transducer for a given supply voltage.
I need to do more work on it (and probably reduce the baud rate) to get it working reliably in real use. Unfortunately I don't have an oscilloscope that I can use in the field without mains power, so when it doesn't work I can't examine the received signal to find out why.