What is the appropriate approach for this problem?

They've been published before. It would be wrong to pretend otherwise. Although some writers would.

Search online for your name, the title of the stories, the magazine's name: see what hits you get, and if you get links appearing but they don't work when you click on them, see if you can look at the cached version of them. They'll be there, somewhere, and if you send them out as unpublished and an editor finds that you lied, you'll have screwed your chances with that publisher for good.

What Old Hack said. It's exactly the same as if the story had appeared in a small print magazine that went bust and you couldn't find any copies for sale - someone, somewhere would still have one, and in any case, published is published.

If you want to publish the stories a second time, you'll need to find a reprint market. Or why not sell/give them away yourself? I've done this with a flash fiction piece that was too short to be worth chasing reprint markets for...

The rights may have reverted, but first rights will have been used up - so the story can only be resold to markets that accept reprints. More common with short stories than novels, of course, because magazines, etc are far more ephemeral.

First rights" are often meaningless. When a story appears in a tiny venue, a large magazine may still accept it, even though they do not publish reprints. It's all about story exposure. Editors don't want to publish stories their readers have likely read somewhere else, but this often does not apply to a story published in such a tiny, low-exposure venue, or to a non-competing market.

Always give an editor the chance to make his own decision about a story.

You should know what rights you sold, any if you sold only first rights, you're fine to submit anywhere else you like. If you sold all rights, however, the story is gone for good. Whoever bought them still owns them.

It's now a reprint. If it ever appeared, even if the website is now gone, it's considered published. Especially as most things are never truly "gone" on the internet. Check your contract to see if the 'zine held onto any further rights, but if it was just first rights, then you're fine for submitting elsewhere.

The number of short-story markets that really care about previous publication is fairly small. Don't worry too much, but do look out for "first publication only" in guidelines.