you have listed some good ways to challenge yourself... i have done the whole using cars till they go BOOM or don't work anymore...
try beating the game without dying... or stealing a minimal of 15 cars or something DURING THE STORY... because after, WHO CARES!!!!! LOL
(note, if you kill someone on a mission and they were in a car... it DOESN'T count as a stolen car... BUT if you kill someone just on the street and take their car, its stealing, Ironic right?lol)