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I understand the frustration of working with a big company where "because it is new" is a reason not to change the site. That is not a good way to run a business but inertia and people trying to protect their own positions often result in this type of situation. And there generally isn't much you can do to change this, sadly. How terrible is the new site? Does your client just not like it? Or did rankings/search volume/leads/sales plummet when it was introduced? If it is the former, your client should just suck it up and stick with the current site design. It is the customers' preferences that matter and if the site is doing well, that is what counts. If the latter then your client is right to want something different but I wouldn't count much on organic search traffic in that scenario. And I don't know that one working piece will drive company success, though perhaps your client hopes to use that smaller success to drive change for the rest of the site. Good luck with that. Either way it solves your subdomain dilemma--in the first case you won't need one and in the second case it probably won't make a difference.

I don't blame you, this could be a large undertaking. Things i would recommend: Make sure you know what the top pages are all on all current sites in regards to external links. You need a list of all pages that have external links and where those are from. You need to get as many external links changed as possible. Redirects are paramount of course. 301 redirects across the board. The content should match or be very similar. In a week or two after launch, check to see how many internal links are linking to old URLs. Do this by crawling your site and fixing any internal 301 redirects. Once you've confirmed the redirects are in place, submit the old sitemaps and the one new sitemap. It forces the SEs to visit the old URLs to find the redirects and also find the new URLs. In a week, remove the old sitemaps. Those are the first things that come to mind. This is a good resource as well https://www.branded3.com/blog/website-migration-guide-building-an-seo-checklist-for-moving-your-site/

Hey Thomas, By a happy coincidence, I just happened to write a blog post on this here recently: https://moz.com/blog/overcoming-your-fear-of-local-landing-pages Hope it gives you some new ideas!