If the website is going to take 1 year to transfer to a new domain, then obviously that's potentially 1 year of not having the new site SEO'd. If the website transfer is very quick, then it's an easy choice! I think it's about finding the balance. You mention link structure changing so I guess you may feel you don't have any SEO to save because of the total new structure. I don't think this is accurate because the site as a whole still means something! You are still potentially a resource.
However, if you start copying it over, then you'll duplicate content. Whilst you probably won't be penalised for this, it is not ideal and leads to confusion.
If you start doing 301's for part of the site, you are going to give Google a headache in regards to indexing. Part of the site is on one domain, but this is part of the site is on another. I'm a big believer in not making Google have to work!
If you can, move the website to the new server over a very short amount of time. And then make it live to the public. Then tell Google the entire thing has changed instead of messing about with single pages. So, may be for a little while you will have duplicated content but at least you can make the site 301!