This will not fit your budget requirements, but you should seriously consider it.

With 6-10 TATL flights a year, the best option by far is get a Chase BA Visa signature card in the US for the 20K signup bonus, and then buy WT+ tickets which you can MFU to Club World for 25K per roundtrip. If you top up your BA miles from other sources (eg. SPG points) you will never have to fly economy (CW award availability is much better than UA business award availability) and you will easily get status with 150 Tier Points per roundtrip. The only question is are you willing to pay the difference between discount economy and WT+ fares, which run around £800 to ORD and less during the sales. Your wallet may not thank you, but the rest of your backside will