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I would create a custom 404 error catcher page just for expired campaigns and 301 the expired pages to it, this way they know it's not a programming error and don't keep looking.

In my clothing retail e-commerce experience, I had much the same issues. Most people tend to search more refined than just a brand name, and men's or women's is a pretty basic distinguisher. That said, I'd do a couple things: 1) figure out what keywords you want to target and make sure your copy's robust and 2) linkbuild. Especially with luxury brands, there are tons of fashion blogs to partner with, and it's pretty amazing what you can get by sending someone an article of clothing.

You said as the old URLs can not be redirected. Then why don't you try for canonical implementation in the important pages to avoid losing link authority that  might have built over the years naturally. The rest of the URLs can be blocked through GWT using parameters. Since you have new version of site, you may want to concentrate only on the new pages. If the old pages are not redirected, anyway you are going to be benefited. I would suggest to go with canonical wherever possible and URL parameters only as a last option. Note: To have canonical, pages need to have more similarities