Oh wow, that's illuminating. Thanks for the detailed info! You've inspired a couple of ideas that I want to experiment with:
I've whipped up a quick mounting bracket for the AS01808AO, which is a similar, but slightly bigger speaker.
The idea is that it will go over the top and then bolt into the PCB from the opposite side and hold it in place. The AS01808AO comes with solder balls pre-added to the pads, so I put into two little windows on the side in the hopes that I can tin the pcb pads and touch the soldering iron to it with the speaker mounted and hope everything bridges. (I will try to remember to post results when I get the PCB).
In the event that this doesn't work, I can buy a spring terminal version of the speaker and modify the bracket to be taller to accommodate the new dimensions of the part. Height notwithstanding, everything else about it should be able to remain the same. Then the mounting process would only require shoving the speaker into the hole and screwing it down on the PCB, no solder necessary.
For the gasket, I want to see if I can try cutting a shape out of electrical tape and fitting that inside the mounting bracket between it and the speaker. I wonder if having something slightly soft and springy will make for a nice, tight fit. Currently I have the speaker inside a very similar mount and drilled to a piece of wood for testing and the sound seems very good so even if the tape doesn't work out, I think it might sound acceptable.
I also bought a sheet of
speaker mesh off Amazon. I want to try gluing a small square of it on top of the mounting bracket and see how that sits.