Printer for new magazine publication

For many years I have been involved with the production of a Chicago-area publication that had been printed on newsprint. It was printed by a company in Wisconsin who only prints on newsprint.

This publication has now evolved to a magazine and is printed on 50# Coated #3 paper (doesn't have to be that exact spec, but similar). We've been printing with a company in New Jersey. We're very happy with their printing service, but have a problem with the mailing (print house must also handle the mailing from our provided list). It just takes too long to get to our readers in the Chicago are. The previous printers (in Wisconsin) trucked the issues into Chicago and mailed them locally.

I've been Googling to look for a new local printer for this job, but am finding so many irrelevant hits that I'm going crazy. Can someone please advise as to how to look for a printer who can print a job with these specs?

Printed 12 times per year; once a month

Approximately 5,000 copies

80-96 pages (self cover); 4-Color Process

Trim size: 8" x 10.75"

Saddle Stich

Paper as listed above (or similar)

Press ready PDFs supplied by customer; no editing involved

Ink jetted address information from customer supplied list with Zip+4 certification

Delivery to local Chicago-area post office

Please give me some ideas how to look for a printer for this job (reasonably priced, of course).

Thanks.