No upgrade on SQ with UA miles I am afraid.

Looks possible with LH Miles & More according to the *A web site:
http://www.staralliance.com/en/trave...de_awards.html

However, this may be LH's out - "upgrades are subject to certain fare class and availability conditions with the participating programmes and carriers"

However, if they won't do the codeshare, you could always have the ticket re-issued (and pay the fee) but I'd check there is availability first!