Your options are pretty limited. You could check with a local freight shipper, typically cheaper but slower than other options, but you'll probably still be eating a decent chunk of money. If you are not willing to eat that chunk, big or bigger, in the end you will cancel the order and refund the money. If you go that route you should message the buyer first, fess up to the error and how much it would cost you, express your intent to cancel the order, and beg forgiveness.
People 'round here don't want to hear that. It is a violation of all that is good and holy where a deal is a deal and reneging is a violation of eBay rules. But honest (even if careless) mistakes are made and simply refunding the money is kinda sorta no harm no foul. You'll probably end up with a black mark on your record one way or another. There is a solution to that which I dare not describe but you can probably guess at it.
As a buyer I had the same thing happen to me a few years ago. I ended up paying an extra $20 for shipping because I still wanted the item at that price and I didn't ding the seller because it seemed like an honest mistake and not a bait and switch. Unless you grossly underpriced a valuable antique you probably won't be so lucky.
As you've figured out by now, shipping one-off items is expensive, a tedious time suck, and even if you know what you're doing ebay can throw you a curveball at print label time or the shipper may fail to deliver on time. There is a "pandemic" of late delivery in supply chains these days.
An item like this, unless it is some high priced antique, is probably best left to "local pickup only". That has its own issues, particularly a sharply limited market especially if you live in a place where there is not a high population density.
Good luck.
