Move WordPress posts on two old sites to two new sites

I am in need of someone to move posts on two WordPress sites. The current problem I am facing is one site has approximately 2,200 posts and the other has about 4,800. I've tried using the WordPress export/import functions, however, it keeps timing out. I have my own dedicated servers running nginx, but even with raising php limits it keeps timing out. The good news is that the vast majority of all of the attachments have been moved to Amazon s3 storage. I would like this done in the next few hours if at all possible. I can provide WordPress, Cpanel and FTP admin credentials (or anything else you need). The completed project will essentially have a duplicate of all of the posts on the new sites, correctly displaying attachments from S3 (there's a plugin that handles it with a simple search and replace if we need to change the domain function).