You could redirect to a page (post type) with a custom template that simply displays your message. Then after acknowledgement and/or a certain time, redirect back to the single post and comments page. The template needs to know what that post was in order to go back to it. An URL parameter is an easy way to do this, but there’s other possibilities.
A javascript solution using either browser history or cookie to get back to the post.
The HTTP referer field might have the information. (or it may be the comments-post page, which is useless– verify)
Store a value somewhere. A transient is probably best, though something in usermeta would work.
I don’t really like the redirect solution, it’s lame IMO to have two full page loads just to display a message. I would look into trying to let the single template try to determine if a very recent comment was submitted and display a message accordingly.