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Not a good idea, I know it's hard to explain these types of things from an SEO point of view that the customer understands. You're going to lose all your good reviews that the business has gained. I'm also not sure if you're able to just create a new GMB once you mark the current one permanently closed without changing the NAP. I agree with SEOman10, work on getting some new positive reviews going.

Also, if the review was not left by a real customer can't you report it to Google or no?

It's really hard to pinpoint the exact reason your jumping in SERPs. Anything you do to your website, adding new content or building a new link, will cause you to jump around. Your process of elimination was good, the video may or may not have had an impact on your ranks. I think it depends on what video platform you used. I'm sure you know Google owns YouTube, if the video was not already on YouTube I would add it to your channel and embed it back on your homepage.

Are you tracking your competitors? If they're jumping around too then it's nothing you did. Also, you may have new competitors going after your keywords recently which may be causing your website to ride the Google roller-coaster. I wouldn't suggest repeatedly pinging GSC to index your website... let it do it naturally. It could raise a flag if your submitting your sitemaps everyday for manual indexing.

I agree with everyone above. A great tool for this may be SEO Yoast Premium. When you create categories that changes your permalink structure it automatically creates a 301 redirect for each page.

Well the general answer is... yes, that can hurt you for sure if you're trying to rank. There's MANY ways duplicate content can hurt you. We had a competitor duplicate our content recently... we sent a well written letter informing them they had 48 hours to take the website down or we would take legal action. They took that website down in about two hours and apologized, stating it was a developer they hired that used our website as a template.

If multiple partners are using the same content and your not currently ranking... your best option is to write fresh unique optimized content. If you're ranking with your current content... then going after every partner duplicating your content might be the better option.