I would do the work around you suggested, entering the amount on Schedule C and then deducting it with an explanation on p. 2. Yes, of course, your client can ask the issuer to amend the 1099-K, and that would have been a really great thing to do seven months ago. I would do what is expedient for me, and call it a day, as my friend Abby says.
Some would say just don't address it on the personal return, let the client get the letter, have a light stroke, (or get mad at you - they do that) and then charge client to explain to IRS what happened. I really can't charge enough to like fixing these things, and the "fix" is going to be saying exactly what you're saying now. Additionally, three weeks after you respond to the letter, the client is going to trot back in there with the letter that says, "We got [one of these six things] from you, and we need two months to let it lay around but we'll get back to you. That's your fault, too. /s