I second @Judas's advice to contact Peter Read. He's a private consultant on Kent school applications. People I know who have consulted him have said his advice has been invaluable, eg in terms of giving them a detailed consultation on which school might suit their child, and what to expect from the applications system, and what your realistic chances are of getting into each. As he's a private consultant rather than a LA employee, I would expect him to be able to advise you even before you've moved.
My personal suggestion would be to accept the place you've been offered, but contact all the schools you would consider individually and ask to go on their waiting lists. When we were looking for a school place at short notice, we found that there was sometimes leeway from the official position. Once schools had established that the sprog in question was a well-behaved one with the prospect of decent results, they started to make noises about seeing what they could do.
Home education worked out well for our family but that was as a first choice option. It's a hard choice when it's not what you really want to do. Social opportunities vary a lot between areas, eg in one area you might find lots of 'alternative' families, while in others the majority of kids at home ed groups could be those whose parents have reluctantly pulled them out of school because they were having serious problems. I wouldn't suggest it in this situation yet - see if you can exhaust other possibilities first, and try whatever school you get allocated and then see how he settles in. It may turn out that actually he gets on well there - OFSTED only tells one side of the story. As others have said above, pulling your child out of school does not give them any priority in getting a school place.
to split my family up and apply to have him go to school in London and live with my dad weekdays which will break my heart.
Don't do this - this is a BAD IDEA! Ridiculous, really. Unless your son has a free place at the best school in the world, no school is worth that.