Honestly with the two daily departures AA has going from the 40-60 gates (as far as I know, at least one of them always?) which are both in the afternoon, it really does feel to me like during those hours you get a good amount of AA pax in the Pier F.
There are definitely way more EXP's on any given AA HKG-DFW/LAX flight than there are DM's on any long haul CX flight.
I'm taking this from my times flying HKG-EWR/SFO on UA a few years ago as a 1K and there were definitely a lot of 1Ks on board those flights!
So a typical Pier F afternoon at ~2pm will have a very heavy number of AA pax in it.
Unless there is a PVG/SIN flight leaving for CX at those 40-60 gates, its highly likely that there will only be 1-2 DM's (+guests) from each flight departing from those gates.
I was more commenting on AA running their own lounge at HKG ala QF. I suspect it works out for AA and CX to use the Pier F and J.
I quite like LH's concept of having your LH/LX F & HON only lounge as you can somewhat compare CX-DM to LH-HON in terms how how hard it is to get there (especially for first timers).
There would have to be an F lounge set up then for AA and other OW F pax (I guess BA since QF has their own). For LH they have SEN lounges as the *A G lounges AND OAL F lounges for non-LH group pax, which are superior to the J lounges. BA has Galleries F to go along with the Concorde Lounge.
So CX would be leasing more space from HKG to stash AA/BA F passengers (and OWEs) and getting no extra money out of the deal. I imagine that is a hard sell at a time when you are losing money...
Also, if part of what makes Pier F pencil out is a bunch of OWE or OW F pax that CX gets paid for...