<<Students must have required courses in Preparing To Vote, beginning (at least) in the third year of high school.>>
How about we begin teaching government (and economics for that matter) in a meaningful way in the third grade -- if not earlier? If the basics are not second nature by the time they reach high school, if not junior high, most kids will have already found other things to interest them and many will never get it, much less care.
In addition to the mandatory voting, there ought to be mandatory registration while kids are still in high school. Much like we give them provisional or student licenses to drive, they should have provisional voter's registration, which becomes effective on their 18th birthday.
Eliminating political parties, although theoretically beneficial overall, has a few pretty serious constitutional problems and would require some reworking of the First Amendment -- a slippery slope that may be worse than the problem it is designed to solve.