Does content flipping make sense to bump content higher if it's already on page 1?

Hi! I am not an SEO expert but have learned a lot on the job in the last year, working for a site that has had very good organic presence in our niche to start.

We currently have a few keywords where we have different content ranking in both positions 2 and 3. That is: multiple posts/pages ranked on page 1, but not in the #1 spot.

We're trying hard to get some #1 rankings back from a competitor. Is this a case where content flipping (adding a canonical from one of those posts pointing to the other) might help give us an edge? Are there other considerations to think through?

Just a bit more context: One area we are losing in currently is backlinks* on some specific posts, but otherwise our pages are competitive or better than the competition, when looking at Moz's keyword tools to get a rough indicator. We already win in DA and sometimes PA according to Moz, but this other guy is still earning position #1 and featured snippets somehow. This is one tactic we haven't yet tried.

*edited to say backlinks on specific posts is where we're losing, backlinks to our domain in general are great