I'm never done with Harris! For a quick bit of fun, I like to fire it up at stage 9 and shop 5, or I'll go for top score and start at stage 4 and shop 5.
I've not put any real effort into figuring out the score mechanics, other than burning everyone to see if you get a big bonus (you don't). I know you get a few points for dropping hats faster, and I assume you get more points for clearing sets of 'more advanced' hats or for clearing two sets of hats with one pair, but my only real scoring strategy is to clear hats and get to the next stage.
By the way, the shop removes hats from the play field, giving you some breathing room if you need it; new hat types are added automatically based on your stage. I rarely ever have a hat sale, instead choosing pass each time.