It is possible to host different pages on different servers; however, the question is "why?" Most sites (and by most, I mean 99.9%) don't even go so far as needing one server to host their site due to the resources that it consumes. Heck, most web design companies don't even have a dedicated server; usually they resell hosting for their clients or refer clients to hosts.
The other question that comes to mind is "why do you have 1600 pages?" If I were you, I'd look into putting at least portions of your site into a database and drawing the information out using a programming language.
Having said all that, a host not offering FTP access is very rare. I can't think of any paid host (except for possibly
Very Sly/No-Value Web) that would not offer FTP access.