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Awesome! Exactly the answer I was looking for. Many thanks, Ben, greatly appreciate the  help with this.

When I was in a similar situation where I didn't have the best of relations with the development company, I used Pole Position's free Code Monitor (https://polepositionweb.com/roi/codemonitor/index.php) to check the robots.txt files of the live site and any development sites/subdomains on a daily basis. I'd get an email if anything had changed, so I could go to the dev company right away and try to mitigate any problems.

I can say this much, I have had a link to my college football blog on my linkedin profile for a long time. In GWT it does not show linkedin as a domain that links to me. In OSE it does not show linkedin as a domain that links to me. So my guess is either they are unable to crawl or find the links in my profile, the links are nofollow, or they simply aren't passing any link juice. Just checked, there are a few links to my public profile and it is http and not https, so it is being crawled and is indexed. The links are not nofollowed. Seems the links aren't passing and juice.