I’m assuming that each airline will give a different PNR, but I may be wrong. I would look at crediting your LX and UA to Singapore Kris Flyer, than converting to VA. I think SQ and DL direct to VA would be best (Not entirely sure, because I don’t have booking classes).
If you really want to credit to a Star Alliance Program, I would’ve have said Aegean in the past (With DL credited to VA), but now I’m not so sure. Have a look at Turkish Miles and Smiles to see if you can obtain any meaningful status there (again, with out booking classes, even in Business Class I can’t give definitive answers).
p.s. without hijacking the thread, what TA did you book the RTW through? And if you have the answer: What is the fare code for this fare?