Surprise seems to be one of the most important ingredients to getting things to spread (I won't quote the academic or anecdotal research of that here.) So I use this inversion analysis often in thinking about coming up with ways of surprising people. My most successful example of this:
I was originally thinking, "How can I get more customers?"
Inverting it I came up with, "How can I lose more customers?" (A different inversion from the OP's but an inversion nonetheless).
Using that as my base I came up with this funny campaign where I tried to figure out how to fire more of my customers. What if I could fire the worst of my customers. So I invented a honey pot website called trickajournalist.com where I described some software you could signup for to spam journalists. And then I used the list of people who signed up for that and banned them from using my product that had an email newsletter component. We didn't want spammers.
It was a nice media/traffic win for what we were doing. And it all came from inverting what we originally struggled to answer.
P.S. If you're interested more in the whole trickajournalist.com thing, the original site is dead now, but some articles about it:
https://www.forbes.com/sites/nathankontny/2018/02/27/trick-a...
https://www.forbes.com/sites/nathankontny/2018/03/08/reddit-...