If it's not the Weber Costello map per se that you are drawn to, but that exact *style*, you could investigate commissioning an original map of the same style. We are generally a community of fantasy mappers, but some of us work in atlas / wall chart / reference map styles, and some do current era work -- if intrigued by the project someone here (or other map/ art fora) could free you from a frustrating copyright search.

What is the size and subject of your original, and what use do you figure on putting it to? If you wish to have closeup shots placing your scenes in a geographic setting, or tracing characters' progress, one might not need a full wall map at full resolution - your areas of interest could suffice, with a lower resolution stand-in for long shots. If you intend to zoom in and out of the map seamlessly, yes, an entire map is what you need. If your characters need a physical prop to be shown consulting, is your one copy even enough? There, repro rights to an original work could be a safety net.

How certain are you that alternate publishers (easier to contact) might not suit your purposes as well?