What would give the better picture quality of 1080i/1080p24 or 720p to send to the Lumagen HDP from a Sony BDP S350? I would then output the HDP at 720p/71.93hz to my Crt projector which accepts 1080i and 720p maximum. Also will a 7inch tube 720p Crt projector accept a 1920x720p/71.93 resolution from the HDP without softening the image?

The general "correct" method is to send source that is not messed with to a video processor. So if a DVD source is 480i, you want 480i to go to the processor (not the 480p that most DVD sources offer).

Blu-ray movies are encoded onto the disc at 1080p24. So send 1080p24 to the processor, and then let the processor do your conversion. Converting from progressive to interlaced is more likely to introduce unsavory artifacts than scaling, since the scaling would be done by the processor, whereas the deinterlacing would be done by your TV, so my gut would say that 720p is a better idea. But, you may need to play with it to figure out which looks best on your TV.