With respect to receiving the underwater pings.
If the pings are regular and for 10 ms every 1 second. Would it not be possible to take the received signal over that period and then sum/pile each 1 second of reception on top of each other 1 second of reception at that frequency in order to improve the signal to noise ratio?
I have done similar things in both amateur radio and also in astrophotography where you sum the received light from night photos to get a better pictures of faint objects. Essentially you improve the signal to noise ratio by doing so.
I hope that the aircraft and ships are recording their reception of the 37.5 khz frequency and time stamping it because later computer analysis using methods such as outlined above could pull out signals that are not audible to the human ear. The news that the Chinese were not recording what they were hearing doesn't sound good however. I hope teh othernatiosn searching are recording all their received static.
The No 1 guy who should be consulted re picking out weak signals like this is Professor Joe Taylor K1JT who is a noble laureate in physics. he has designed software that enables a weak signal of less than a watt to be heard and identified/decoded on the other side of the world.