If a reviewer makes significant contributions to improving a paper, may he/she suggest becoming a coauthor?
At this point, I wonder what the best way to proceed is. Should I just submit the report with these suggestions?


This is indeed the high road to take here. As a reviewer, you explain your ideas on how the paper can be improved. The authors will or will not take all or some of them into account.

Asking for co-authorship in return for your service would likely be perceived as very cocky and unprofessional. I doubt that either the editor or the authors would be pleased about this or seriously consider taking you up for your offer.