To corrupt the vote, just offer some money for every empty ballot that gets sent to you to fill in and mail. There are a lot of people who would trade their ballot for a $20 bill.
If you picked the right districts, it wouldn't even cost that much to tilt the votes in your favor. At $50/ballot you'd almost certainly get 11,000 extra votes in Michigan - enough to swing the state in the last election at a total cost of just over half a million dollars.
This ease of abuse is one of the many, many reasons that I support a single, national vote for president over per-state winner-take-all electoral college voting.