If the display accepted 720p in over HDMI, then it would just work already. Since it doesn't it also isn't going to scale that image to 1080i, as it won't know what to do with the incoming signal. Chances are that the only 720p it knows what to do with is 720p from it's internal antenna tuner, not from external sources.
So, what you need is a scaler that accepts 720p HDMI in, and spits out 1080i HDMI out. A lot of receivers should be able to take care of this for you these days, or you can pick up a separate scaler. The problem that you are pretty rapidly faced with though is that cheap scalers kind of look like crap and introduce some pretty serious lag, and good scalers/receivers are probably in the "just replace the TV with a 42" plasma/32" LCD" price range.
Your best bet really is to just play your games at 1080i when the PS3 will let you, and play the other titles at 480p until it's time to buy a new display. Everything else is likely to just degrade your experience, make life a hassle, or make no sense from a financial standpoint given the alternative of buying a new display.