Nearly any old Schwinn can be converted. It is made easier if the bike in question has long, horizontal dropouts. I'm familiar with many old Schwinn's in addition to the Paramount that would be good candidates and are very well made. Those would include the Superior, Sports Tourer and Super Sport to name a few. They were among the lightest that Schwinn made at the time and the quality of manufacture was very nice.

You can find catalog scans on Tom Finley's site which can be accessed through the Waterford site.

https://waterfordbikes.com/w/culture/schwinn-catalogs/

Also, have you checked out the conversion information in Sheldon Brown's website?

https://www.sheldonbrown.com/fixed-conversion.html

Edit: P.S. Unless you insist on paying more for one, I'd check your local Craigslist for candidates first. I don't think the bay is the best way to go.