The old school Mitsubishi CRT RP HDTVs do not support 720p...so you could try all you want, but I doubt you'ld see anything if you set your 360 to 720p.
Stick with 1080i, my girlfriend's parents have a Mitsubishi like yours and 360 looks great on it. Plus, 1080i is superior to 720p so I don't see why you'ld want 720p anyways.
To fix your black and white levels, you should calibrate your HDTV. Pickup a copy of
DVE, it'll be well worth it. That'll help make sure your shadows and other black details look right...not to mention give you a much better picture in general that is closer to what your HDTV looks at its best.
Also, a CRT can give you one of the best pictures out there. Yeah they have their issues, but when setup properly...their picture is hard to beat...even by the best plasmas and lcds out there.
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Optoma HD70, 42" Panasonic TH-42PX75U, Denon AVR-3805, KEF KHT2005.2, Panasonic DMP-BD55k Blu-ray Player, Monster PowerCenter HTS-3500MKII
BeyerDynamic DT990, E-MU 0404 USB, RockHopper Mini^3, Grado SR-80, Cowon iAudio X5, Acer Ferrari 4006WLMi, T-Mobile G1(aka HTC Dream)