It's my understanding that the restrictions on changes depend in part on where you purchased the ticket. From Australia (and from most countries, except U.S.) I know that if you haven't started any of your travel, then ANY changes can be made (even your 1st intercont. segment). The changes can be made because when originating in these countries, the RTW tickets are fully refundable pre-departure. If, however, you HAVE started some of your travel, then the first intercontinental segment (even just date/time changes) can NOT be made. In addition, all segments leading up to that 1st intercont. segment can NOT be changed.

travel.com.au can be useful for reading rules on various RTW fares, including of course Star's.

Question for you: How much did you pay for your UA/CX RTW fare originating in BKK. Were you able to purchase it outside of Thailand, or did you have to pick it up there?