Well, I'm going to back you up for a minute, just to illustrate a big (quite big) alternative, an actual RTW ticket.
As you may know, RTW tickets are priced differently depending on the country of origin and purchase. In the case of Oneworld, the Oneworld Explorer RTW ticket (and note AA hugely confused things briefly when it gave its now-defunct Oneworld award the same name) is good for up to 16 segments, valid for a year, has no mileage limit, and the price is based on the number of continents touched.
In your case, that would be three continents, North America, Asia and Europe, the minimum number for a Oneworld Explorer. The ticket comes with a lot of rules, including a maximum number of flights per continent - 6 for North America, 4 for all other continents (plus of course the intercontinental flights.)
Now you're looking at an out-of-pocket cost for your itinerary in the neighborhood of $4000 by the time all's said and done, for JFK-HKG-CMB-BKK-SIN-FRA-JFK, six segments and around 23,000 miles, of which about half would be elite qualifying or mileage earning on AA.
But here's the deal. How much traveling do you do, or would you like to do, in North America annually? As an FT member who went for the Plat challenge on AA, I'm guessing the answer that you DO travel a bit over the course of a year, maybe a lot.
So, thought experiment. What if you used enough miles (or even bought them - big bonuses on miles now available from AA/US through the end of January) to get yourself to Tokyo, and started a DONE3 RTW ticket there?
Right now, because of the strength of the US dollar vs. the Yen, a DONE3 bought and begun in Japan costs around $5500 plus taxes. Now, yes, that's more than your projected spend for your trip, but instead of
this route in a combination of PE, business and economy, it could give you something like
THIS instead. (And of course that route is totally imaginary - there are probably tens of thousands of permutations.) Basically, start in Japan, do your Asian and European flights, then fly home. Over the course of the remaining 12 months of the ticket's validity, travel around North America, Central America, or the Caribbean, all in J or F, before returning to Japan to finish the ticket.
Note the same scenario holds if you bought the ticket in a relatively low cost city in Europe/Middle East, such as Cairo (a couple hundred bucks more than Japan.) Fly into Cairo, don't even leave the airport if you want, then start the RTW there, maybe by flying to Amman or Doha then across the pond to NYC.
The Japan-origin trip, which is pretty conservative by Oneworld Explorer standards, would earn you more than enough elite qualifying points to retain Platinum, probably something approaching 100K redeemable AA miles, and, depending on your actual travels, a lot of butt-in-seat miles in business or first class (with DONEx tickets, flights on 2-class AA domestic flights book into first class, with the appropriate class of service bonuses.)
At, say, $6K all in (counting taxes and YQ) that would average out to $375 per business- or first class segment over the course of a year. By anybody's metric, that's a hell of a deal, but of course it presumes that you have the need, or the desire, to fly that much.
And if you have the time resources, you can even beat that deal by making your way to South Africa, where a DONE4 - four continents, business class, costs right around $5000 plus taxes/fees, for something like
this.
A number of us use these products in a "strategic" fashion - a paid RTW every other year, burn the miles in the following year, repeat. The numbers can get very compelling.
If interested, consult the Oneworld board for more details - lots of useful information over there.