How do I address my research publication being 'scooped'?
You cannot speed up the publication/review process. Suggesting to an editor that they need to speed up the process because you might get scooped is inappropriate. In the future, you need to choose a journal with a better turn around time. Assuming the majority of the time the manuscript was with the editor/reviewers and not on your desk being revised, you can, and probably should, complain to the journal that their review process is too long. Explain to them you will no longer be submitting to or reviewing for them.

In terms of being scooped, your concern of the other authors having access to your manuscript is a valid one. The editor of your manuscript can easily check if one of the reviewers is an author of the competing. In the case where the reviewer shared the manuscript with one of the competing authors, things are more difficult to "prove". As you only became aware of the competing manuscript as a reviewer (which hopefully you turned down), even talking to the competing authors is difficult. You probably should contact the editor of the competing manuscript as discuss the issues. The editors can then work together to try and resolve the issue.