Would it be possible for the 'cheater' (for lack of a better term) to choose which transaction got confirmed after the result of satoshidice was shown?
Yes. Normally Satoshi Dice sends back its results a few seconds after you placed your bet. If it was a loss just try to get your double-spent transaction confirmed before your bet becomes confirmed.
Just use no tx fee on the bet, and some huge fee when you double spend the coins to yourself.
To reinforce this scheme, tell the miners they can make hundreds of BTC from this - I am sure some will prefer your huge fee txs over the free once ;-)