Is this department store one you shop at otherwise? Because honestly, gift vouchers to a store that doesn't carry the thing you really want are useless unless they do carry other things you would actually plan on buying for yourself. Not just stuff you could buy, but stuff you would buy in the future.
Because the best outcome in all of this is that you take the cash equivalent of what people had tried to spend at the department store, find your dinner set somewhere else, and buy similar pieces yourself. If you can't get actual cash from the department store, but you would have spent an amount equivalent to the gift vouchers there eventually, then you can just use your own money and all is well. But if you wouldn't otherwise have spent that amount of money at the department store, then gift vouchers are rather useless to you and you might consider pressing the store for an alternative solution to this problem.
I'm also curious how many people tried to purchase things off your registry, and how close to you or your fiance they are. And also if the department store would be willing to issue refunds to the original purchasers. Because if a close friend or relative came to me and explained a similar situation, but told me that the store would issue me a refund and they were registering for the same dinner set at a different store, I'd absolutely take that refund and go buy something from the dinner set at the other store. My goal as the gift giver would be to give the bride/groom what they actually wanted, and as long as it wouldn't require lots of convoluted steps for me to get my money back and buy the thing from the other store, I'd be more than happy to do that.
I wouldn't personally be comfortable asking anyone but a close friend or relative to take a refund and use it somewhere else, and I think how I'd react to that as a gift giver would sort of depend on the circumstances. But if there aren't many people who have tried to buy off the original registry, and they're all close enough to you that you talk to them on a regular basis, you might ask the department store if they'll issue refunds to the purchasers if they refuse to issue an actual refund (in money, not gift vouchers) to you.