This guy is unreasonable and it sounds like you've done what's required to make it fair considering a.) the transaction was a year ago, b.) you offered to refund the original price, c.) although you didn't assay this (which would likely hurt the resale value), it was stamped 18K and was sold in good faith. If however, Peter said he assayed it as 18K and it wasn't, then there is a real problem in claiming one did an assay but didn't. Regardless, it was your mistake [Peter] not to assay it--you must always know your product, imagine if this were 22K (obviously stamped karat never runs high!). I understand this is very difficult to do without marring the piece and that everyone's idea of an assay is different (i.e. some people want fire assay, some will accept XRF, some will accept touch stone).
He should be reimbursed for what the agreement was--a year is a stretch, and it's obvious that he only mentioned it when he went to sell it and had someone come up with a different number. I'd be upset if I were him, and I would certainly expect my money back either in full, or in gold as per the original agreement at its value on that day of sale. Expect more than your fair share of monetary compensation in this case after so long seems a bit unfair. I don't know all the details, but if it were gold for gold, or gold for cash, it should be valued at the time of sale.
And Peter, this business is such that you'll never make every client entirely happy. This business, above all, is a service business and you are only as good as your reputation earned through exemplary service. Some might consider this bad business, but even if it costs me out of pocket, I'll make it right to my client if the error is mine. I try to be a reasonable fellow and treat clients how I'd like to be treated. I know what it's like to have been bulldogged by refiners and treated as an *****. It's infuriating.
You have to do your best to upright, honest, and fair and put your clients before the bottom line. At the same time, you'll run into clients that can not and never will be made happy. Why? They're not grounded in reality and believe things are there when they aren't. Here's the real scoop about this business: everyone (especially beginners and people who are really hard up) thinks what they have is worth more than what it is. I've been guilty of it, you've been guilty of it, your clients, and mine. It's bias, pure and simple and is a function of psychology. I do my best to make clients happy, but I have run across several that I don't want to do business with, irrespective of what they bring me and how much I could make off of it. They're unscrupulous, irrational, and irascible and frankly, a bother to do business with because I already know they'll be trouble. I'm not trying to put one over on them, but they've clearly had such a bad experience with everyone, they assume it to be par for the course and are out for revenge. That said, they're trying to put one over on me.