Great question here.
Given that you may have a lot of fake fans (this is why I always caution clients about inviting friends to like their page, or running FB Ads to get likes) it might actually work against you re: FB’s algorithm thinking that your content must be low-relevance because you’re getting such low engagement. However, with FB Ads, you can create a specific audience of “people who have recently engaged with my page” and so you might be able to bypass that algorithm hit… but that means you pretty much need to be spending Ad dollars on every post. You don’t have to spend much though… just $5–10 per post could reach all of your current engagers since it’s a relatively small number.
For now, try that, just keep the biz page, create a Custom Audience of those who have engaged with your Page, and boost your posts just to them (not to all your fans.)
And yes I would recommend letting go of your FB Group…
Let me know if that helps!