You have a price in mind? I agree with the other posts to consider the IWC Portugieser line over the Portofino.
Other suggestions:
- Breitling Navitimer B01 (not quite in white, but some adjacent colors are available)
- Patek Philippe 5270J - not quite as thick as you want, but satisfies the rest of your requirements
- Used, but what about the Omega Speedmaster Silver Snoopy 45th Anniversary edition?