Other Hotel Programs - Ritz Carlton- can I somehow earn AA miles?

I'm staying at a Ritz Carlton in Istanbul. My favourite loyalty programs are AA Advantage and SPG. Is there any way I can earn towards either of those two programs? Is there an intermediarry I can transfer thru?

Ritz Carlton is owned by Marriott and the rewards programs are substantially the same. You can earn British Airways miles, which are redeemable for travel on AA, or you could earn US Airways miles which can be converted to AA miles through points.com, but with a substantial loss in value. (It appears that 1,000 US miles can be exchanged for 219 AA miles, but I have no balance in my US Airways account, and I haven't used points.com in a long while and do not profess to fully understand the options.)

As the post above states it's a complicated and rather loss making enterprise. I just keep the points I earn on Ritz Rewards and use them for free nights when I can.