Power sounds alright. If nothing else pans out it might be worth opening the old ECU to see if you have a swollen or leaking capacitor. Shouldn't be the issue in '02 but easy check if you already have it out.
ETCS makes more sense than ECTS for a start issue. Check the DBW connections? My 3.4 is a 97 throttle cable only can't help with specifics.
Only time I had to mess with an immobilizer was when I lost my only key to an LS so had to get a locksmith involved anyway. You might try doing this -
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