I think
C
chocolatejr9
has the right idea with tying it to a specific Nintendo account. Register your copy of Super Smash Bros. Ultimate to your Nintendo account, then spend your 9 votes wherever and whenever you'd like using whatever devices are most convenient to you.
Obviously, you would get one ballot per copy of the game and Nintendo account, so you can't just create a bunch of accounts to stuff the ballot box over and over again. I suppose someone could buy additional copies of Smash Bros. Ultimate AND make new accounts if they really wanted to fortify Gex's chances or whatever, but you wouldn't be able to really tilt the needle in any meaningful direction without investing a stupidly high amount of money in this endeavor.
It's true that the last ballot also mentioned that the data would be used for future projects rather than Smash for Wii U/3DS, but I also saw a lot of people who missed this point and got upset that the ballot didn't impact the entire direction of that game's DLC. I think really hammering it in that the results of the ballot will not come to fruition for a while is still important. It's kind of like how Ultimate really emphasizes that the clones are largely extras that don't take development resources by branding them echo fighters. This wasn't new information, but it was much more clearly communicated to the general audience this time.
I'm not entirely sure I understand your point about the second and third rule feeling contradictory. Rule #2 is a security measure to ensure that people don't just write programs to ensure their favourites get continual and consistent votes. Rule #3 is to prevent scenarios where voters choose who they think has the best chance of realistically winning rather than who they would most like to see. Its purpose isn't to really provide individual votes for multiple users of the same copy as it is to ensure that voters don't self-censor. Both rules are in place to ensure that the results legitimately reflect the player base's genuine desires.
I will admit, I don't really see a way to allow multiple users on the same console to get all 9 votes that doesn't come with some major drawback. Creating Nintendo accounts is free and relatively easy, so tying suffrage to that would really just be the anarchy of the first ballot with an extra step. Likewise, as
Rie Sonomura
mentioned, tying suffrage to an IP address privileges those with multiple devices. I suppose the next best solution would be manually registering voters like in a real election, but that kind of becomes a logistical nightmare when you consider that people will be voting out of numerous countries with numerous languages and Nintendo still wouldn't have a way of verifying that everyone is going only once without doing something crazy like asking for ID.
So, it's definitely far from a perfect system, but I still think it is (broadly speaking) the best option available.