I haven’t the exact answer to your question, but with OwlStat you can analyze a post and its engagement over the time. You don’t have to insert your username or password, just the post URL and It could be useful for this kind of analysis: i.e. you can insert the post you upload on the ‘post analysis’ section, and look at the graphs that shows the likes/comments. So, if you do this with every post you upload you can see the common results on your posts and check what could be the best time to post.
Hope I’ve helped you in some way
Ps. It’s a function that it’s only in the dashboard. With the free plan you have just 1 analyzable post, but if you want to test this function I can enable you to track more post for testing (free) or I can give you a coupon for this service!