It seems that you accepted a voluntary downgrade in order to get rebooked to the LX flight. Most likely you could have insisted to be rebooked into PE by waiting for a different/later flight with PE. Did you ask AMEX Travel to rebook you into a flight with PE available?

If SQ cancelled their flight it seems to have little to do with LH - LH issued the ticket? (it was on 220 ticket stock?)

SQ flights from SIN to Europe are not covered by EU Reg. 261/04. Neither LH or SQ is liable for the downgrade under EU Reg.