WP to WP Transfer API?

Does it exist?

I always have big issues trying to migrate WP blogs to new installs. The problem is that on WPEngine we are limited on memory and our sites are huge. I can’t export all content without an error and I can import large files without an error. I cant do sections of posts because that option wont export images. Even with SQL dumps theres a lot or rewriting involved and it occurs to me this should be a whole lot easier!

Does a plugin exist that does the following:

Have a cross blog transfer where by the old & new blog have a plugin installed and via an api they go through all content in batches of the users selection ( one at a time if need be ) and transfer each post, page, images, etc. to the new blog.

Thanks,
-Bill