The big issue I see is that your itinerary crosses the cutoff of nearly every FFP in OW, so some of your itinerary would be in one year and part in another after the reset, that's of zero use for status unless you already have some other status points in that program to build on.

The only one I know of that still has a flexible year based on your first earn date is QR's. It's pretty easy to get QR Gold (OW Sapphire) on an itinerary like this but would need to check how many QPoints you could get toward the 600 required for QR Platinum (OW Emerald).

Just to be clear, the airlines you've mentioned are the codes you're booked on or the operating airline? In OW, the actual airline codes booked on are the only thing that matters (as long as it's a OW operated flight).

If you're booked on a ton of AA and BA codes as indicated in your itinerary, then AAdvantage is absolutely the worst program to credit to despite what a couple of others have said. I'd actually like to say they're trolling you but they are both very reputable members here.

Sometimes AAdvantage does credit RTW fares as distance, but it seems to be getting rarer and often they'll credit on a revenue basis and you'll be given an absolute pittance (5x-11x based on status) compared to what you'd have gotten on a distance calculation with a different airline's code (Basically for AAdvantage you have to avoid any AA, BA, IB codes and I'd bet within the next year, AY also). As a base member you get a paltry 5x of revenue assigned to that sector, basically consider that something near zero on a RTW.

Without running numbers yet, my initial reaction to your itinerary if this is your only OW flying is probably QR and maybe AS. You wouldn't earn enough in AA to be meaningful with that many AA and BA segments.