No, the CRT doesn't tell me, it just displays them all (except 1080p?) When you setup HDMI, it checks to see what is the highest your display is capable of, and it came back with 1080i on mine.
You have to go into the display settings in the PS3 and set the output type and resolution, which would be 720p in your case, and since the projector is 720 native I don't see why it wouldn't work. To do the initial setup, you have to use composite because that is what it defaults to, but as soon as I switched to component, I could tell the difference right away. Resistance in 720p looks pretty impressive.
Was Superman the BD verson or DVD version? The PS3 does not upconvert standard DVDs to 720p, so they will still play at 480p AFAIK.