I wouldn't dismiss the TLI 'window' too quickly. Earth launch times were set to get the moon in the desired position (with not a lot of leeway, although I don't remember specifics). Further, earth launch windows were limited to a few days each month in order to have the moon in the necessary position - they couldn't launch except for those days.
I took a class back as an undergrad on orbital mechanics - but I didn't do very well at it (the guy in our class that did ended up with a job working orbital mechanics - apparently if you 'got it', companies that did that sort of thing found you highly desirable).