As I think you’re already discovering, the airline with the “most value” is the airline that you can book the seats you want with! Yes, Asia Miles will take the fewest points, but if you can’t get flights with them, then they don’t have the best value after all. You might like to look at KrisFlyer: Singapore Airlines availability is generally pretty good, and their fees and charges are low as well. But if a seat you want is available, you’re getting the “most value” from your points.
Having said that, I was a bit surprised to read that you can find no availability on Asia Miles. Asia Miles availability is there if you know how to search for it. The trick is that they release a very small number of seats, 352 days in advance, at midnight, Hong Kong time. Very often, all those seats (I’m talking about the cheaper “Standard” awards) are gone within a day or two.
Last month, I successfully booked an Asia Miles business-class redemption to Europe. To get the seats I wanted, I set my alarm for 3am (AEST), got up and booked the seats within minutes of them becoming available, and went back to bed. Don’t wait for your return trip to become available: book the one-way trip as soon as the seats are released, 352 days ahead.
So my advice would be to try first for an Asia Miles redemption; my second option would be Singapore. If you still can’t find seats, that’s when it’s time to search a bit further afield (eg. Emirates/Qatar/Etihad, Thai, Malaysian, etc etc… I think Air France also codeshares with Qantas from Singapore). You’ve got oodles of points and you can use them on countless airlines. With a bit of diligence you shouldn’t have too much trouble finding the flights you’re after.
Let us know how you go!