That is such a simple mechanism, yet can be so frustrating.
I know you said you checked for air leaks, but two things caught my attention; one is the missing chunks from the edge of the casting body near the lower port, If you haven't already done this, I still think it's worth a quick perimeter wrap of painters or masking tape along the whole perimeter, except of course for the whistle ports themselves. If there were multiple air leaks along the edge, it would be quite difficult to momentarily seal them all with your fingers., whereas the tape works great!
Number two: your gasket has a suspicious appearance - the dark areas show where it clearly sealed, yet there are areas along the outer edge and almost all of the internal edges (or walls of the resonating chambers) that show little or no sign of sealing. It's possible when reassembled (as it currently appears to be) a good, solid squeeze between the cover and the whistle body while the motor is running might suddenly produce that second tone you are looking for! If it is an internal leak, then your test for "housing leaks" (including the perimeter painter's tape) might not have revealed anything - but I would still do that step first to insure a good perimeter seal for the squeeze test.
If you've already done all this, well.... I'm officially out of ideas. Maybe the next step would be to hope for the best at York. Let's also hope there IS a York this year!
