I'll just throw out a technique I've used to knock down the cost of premium cabin travel - might or might not work in your case, and probably would require you to move to Oneworld rather than UA/*A.

Oneworld's main RTW product, the Oneworld Explorer, unlike Star Alliance's or Skyteam's RTW tickets, is not mileage based, it's continent based. 16 segments, good for a year.

So an example: RTW fares vary hugely by country of origin/sale. Right now a 3-continent business class Oneworld Explorer bought and started in the US costs $10,964 plus fees and taxes. The same ticket, bought and started in Japan, costs $5532.

The ticket limits the number of flights per continent (6 in North America, only one a transcon, 4 in all other continents.) And changes of ticketed points requires a $125 fee to reissue the ticket.

Hovever here's an imaginary example (probably millions of variations) of a 16-segment RTW ex-Japan that would probably cost around $6200 after taxes, or something like $388 per premium cabin flight. (Note in the US a business class ticket puts you in first class on two-class flights.) That's a good deal for SFO-LAX, but a screaming deal for HKG-JFK by comparison.

And if you want to go farther afield in your travels and can use miles to get to, say, South Africa, then you could start a 4-continent itinerary like this for around $5100 plus taxes and fees.

And of course this amount of flying in premium cabins will put you into elite status almost immediately, and you'll earn enough redeemable miles that some of your premium cabin travel the following year will be on the house.

Up until a year or two ago (when my flying became very curtailed for family reasons) I was buying a 4-continent RTW every other year, flying on the ticket in year 1 and using miles for year 2, rinse and repeat. (Obviously there are cases where you need to fly outside the ticket, but you're still money ahead.) On average over 2 years I was flying something like 22 first- or business-class segments for around $6.5K out of pocket, a pretty good number in my book. It requires putting together something like a "two-year plan" for travel, but the options and freedom make that a pretty pleasurable task.

If interested, plenty of information on the Oneworld board.