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There are a lot of gas stations out there, and in a real zombie apocalypse we're talking, what, 90% of the population dead? And many of the remaning 10% not driving cars around, and those that are are probably running on gasoline? Getting diesel is not going to be an issue.
And yeah long term I may own something like one of those as a ski RV (overhauled for sleeping quarters) but it's probably 5+ years out.
Growing potatoes: good, but you need to eat more than just potatoes. You'd want to grow a variety of vegetables and fruits. Islands in BC are fine for running a garden and orchard. Just kill and eat any deer.
Small log cabin: not ideal. Also, keeping most of the island forested is pointless. Are you hoping to hide? Zack doesn't care about trees. You want visibility. Now, if you were to create a treetop cabin 30 feet off the ground, I'd be with you.
Firewood for cooking and heat: also not ideal. You want a generator and insulation. For one thing, the smoke from the fires is a dead giveaway for people in boats who might be looking for someone to raid, since the people who will inevitably try to flee by ocean will quickly run low on supplies.
Zombies can travel through water. They just can't swim. So one of the issues with an island is you may all of a sudden have 1000 zombies walking up onto the beach. It certainly helps, though - the further out your island is, the less likely it is zack will make it out there. Also, if you're seriously in the middle of the pacific, the pressure at depth will effectively destroy any zombies that head out there. That won't work for coastal islands but it is a reasonable plan, if you have a means of getting to such a place.
Zombies can survive without breathing all of the sudden? Thats a bit of a leap
And it's not a leap at all man. You need to read World War Z. It's absolutely essential.