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I think it is pretty dependent on the content. It sounds like an overly simplistic answer, but I'd consider using the date when it is time-relevant content and not when it isn't.  That way you are only showing relevant, useful content to the users - which has to be good for all. If it helps with CTR from the SERPs then all the better! Google knows (at least roughly) when the content went up whether you date it or not, so it really is about what you are showing the user both on page and in the snippet. So why bother them with it if it isn't relevant?

Mind shooting over the Query and URL in question? I'd love to take a peek directly.

So despite the different look and navigation you recommend migrating the whole site to a subfolder on our subdomain? If you own this site now I would suggest you take some time to investigate branding. A standard look and navigation is desired. On the other hand, you need to be careful making changes to successful platforms. Based on what you have shared, the likely recommendation would be to use a subfolder, but a proper recommendation on such an important topic cannot be offered in a Q&A. A SEO would need to learn about your company, your business, your niche, the site you are absorbing, etc. prior to making a decision.