I take some issues with your second two paragraphs—for instance, a lot of folks who should be able to vote aren't going to have a cable bill, and depending on household situation some might not have any bills in their name—but altogether I find your first paragraph a sensible representation of the sort of compromise to which I'm very amenable (and—despite those protestations of the recent, sturgbot-9000 version of sturg—I am pretty willfully amenable to compromise).
However, I would add one very important caveat to your proposals: the first policies ("free government ID, year round registration, longer times before people fall off the voter rolls, extended early voting, and more polling locations") must be implemented before the second set ("ending third party registration and requiring proof of citizenship") or you're simply effectively disenfranchising a statistically-significant number of potential voters in order to deny the franchise to a statistically-insignificant number of individuals who shouldn't be voting. But if you can get that first litany of policies enacted, I'm all about rubber-stamping the second set.