They are moderately happy with our solution. How should the customers approach the potential suitor?
What an interesting concept (and I'm being polite with the word "interesting').
Your customers, who pay for your service, should do the leg work to be your cheerleaders for your business so that you can lock in your Biggest customer (the end business buyer)?
There is absolutely no reason your customers should be talking to the "potential suitor" in a cold call (they make the outreach) scenario.
If it's a "suitor" (they are pursuing you), then they already have interest.
Your focus instead should be on how to turn "interest" (which is about as a common as bad ideas) into "motivated interest". The subtle difference being that they have a specific, motivating reason to pursue the deal with some margin of urgency and seriousness.