You are placing the goalposts in such a way that your argument is the best one. "assuming that zombies can't swim/walk at the floor of the ocean, or if they can that they aren't smart enough to seek out humans this way"... I see no reason to assume that. If zombies are undead why can't they walk over the ocean floor?

As much canned food & water as possible
A large arsenal of weaponry and ammo
Books, writing material
As many people as possible (men & women)
Sperm from sperm banks to prevent inbreeding
Infrastructure & tools (solar panels, nails, timber, steel, etc)
Seeds & possibly livestock

How will you get all these things if infection rate is 100%? You will need to go about town collecting these things for a long time, they ar enot things people have just laying around there house. When doing so you will endanger yourself greatly to getting infected. Now to mention how are you getting to the island with all these things? How are you loading them onto whatever boat you have? How are you getting that boat? And if you find a boat large enough to carry all these things do you know how to sail it by yourself?

You are assuming too many things for this argument to be a realistic one.

and establish a perimeter, slowly expanding until the entire island was clear of infection and self-sufficient.

How would you do this?

Going by your way of presenting the argument you might just as well argue "I will barricade myself in my house with an entire army, an arsenal of guns, enough food to last me a lifetime and a bunch of playboy bunnies to procreate. Oh and also the zombies can't walk fast or climb or get into my house". It's an unfair way of setting the parameters of your argument.