Zephyrana
You seem like a very reasonable and understanding chap(ette) and have put up with a lot.
Here's some thoughts I have on this issue, as posted:
1. Isn't there supposed to be a oneworld team at LAX dedicated to monitoring and protecting such connections? Perhaps they think QF18 to SYD and then onto MEL equates to getting you there as quick as possible (ignoring the F part, which is not right for a paid pax). i also suspect their own mandate (if it's a oneworld team, or QF ops) is to keep "their" pax on their metal to cut costs. If they handed you over to AA to LAX, that would incur a fair cost to them (not the pax's problem of course!!!) and of course there may have been no availability by the time this was considered (though given the flight time LAX-JFK, they'd have known probably 4-5 hours prior to check in this would be an issue).
2. Astounding the attitude of the BA staff at JFK. Yes, they "handle" QF at JFK, but they clearly have little to do with QF. I wonder if QF even have a real QF rep on site. Judging from the attitude you received, it seems either they do not, or the staff were not willing to entertain to get hold of the station manager (or whoever).
3. You darn well SHOULD be important to QF!! Forget if you're Gold or Plat but paying a F fare (evem if it's Saver, or A class) is still a massive premium and yield to QF. on that day you would have been one of their best customers revenue wise. That deserves better treatment in my book.
4. Did you try to contact QF USA res when you were at check-in? I know they have a poor rep, but perhaps more proactive/useful thank the BA people weren't. (I admit, time may have been an issue at this point)
5. Simply saying "come back tomorrow and try again" as one's only option is poor.
6. Re the refund, you did not say (or I may have missed it!) if this was just a oneway fare JFK-MEL, or part of a roundtrip that could have an impact.
7. I'm glad you had little trouble with the ORC and it seems like QF's follow-up has been better at least.
Given you say you were Gold then hopped over to Plat during this latest "adventure" you've clearly already flown QF at least a bit in the last year - I hope your other experiences have not been so poor.
my 2 or 3 cents
best wishes,
richard