You should just call LH and book the Thai segments. I actually didn't have much of a problem on my last trip booking directly with Thai also with a LH RTW ticket. It only involved some domestic TG segments. The old rule.... hang up and try again if you get a bad agent.

On this trip I even found that LH had D inventory on SQ whereas SQ told me that it was zeroed.

Also, you should call LH directly in Germany; they are much better. I am not too fond of the Long Island (or New Jersey?) crew. Actually, if you call late at night in the US they connect you to Australia.