This is an amazing coincidence. I was one of the publishers of Zonepress and Zone Magazine. Which piece is it? Ultimately, it would be the writer, not the press you'd need permission from, as we would have only had first serial rights. If you can let me know which writer I can see if I have any info that can help you track him/her down.
I do believe that you are correct in your last assumption--no permission, no go, failure to find copyright holder wouldn't protect you from future action.
I wrote the first piece in that anthology, by the way.
You may be right about 1979ish being the end of the small press side of Zone. Zone Magazine went a few more years, albeit irregularly. The journal moved from Brooklyn to the East Village with me in 1979.