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I've had a similar scenario with Yoast - re: adding the site name (in this case, site URL) to the title automatically, but not really registering that fact when you use the plug-in on each page/post.

If it were me, I'd advise against 2, because you're right, it does look kind of redundant & spammy. OR, if you want, you can turn the setting off that automatically adds the site name at the end of every single one of your titles, and then just add it manually so that Yoast does register it. In WP, these settings can be found in the Titles & Metas section of your Yoast SEO plugin (accessible from the menu on the left, right under SEO's dashboard).

I hope that helps!

I saw an interesting article from Razorlight Media about this topic a couple of months ago. I've linked it here for you, as it might show some kind of evidence regarding how Google treats post dates with a real-world example.

Honestly though, I've found that if the content is good, has a high DA, and is consistently receiving traffic, it shouldn't be an issue. That being said, is there anything you can do to update your material that would warrant an updated date (without affecting the URL, of course)? That might be something you want to consider to show other readers that its still extremely relevant material and is regularly updated.