Hey Eric,
No, you're right. If that's the degree to which your content is diverging, it may be necessary to have 2 completely separate domains. One set does not have anything to do with the other, and that will absolutely affect relevance and compatibility when it comes to linking practices.
You could go with a subdomain structure and diverge your link profiles - it would have much the same effect as going with 2 separate domains. That being said, it makes life really difficult if you are moving domains or redirecting in the future, so a subdomain structure is pretty permanent and not ideal if most links are coming back to your Home Page.
You could attempt a social media bridge for both sites, but that may be a bit beyond what you are trying to accomplish here. I think you have the right of it based on the facts presented.
Here's wishing you the best of luck on the shift!
Best,
Rob