I can open all files in Zotero just fines. They are not linked (well, a few, but most are PDF).

None of the few exported files transfer on import, for instance to Papers.

Ok, I made a stupid mistake –  I launched from a wrong Zotero Library (from which I had culled most pdf's earlier.

However, the import problems described remains with the correct library. While all pdf files are now exported fine, they still dont import to Papers. Only the references are imported.

Export to bibtex and import without files work fine.

This is a thorny issue. The problem appears to be that at least Mendeley (which is the only one I can test with) will only import attachments from absolute paths. That means any import/export can only work on the same computer.
Zotero's export uses relative paths (that's why it exports the files into the same folder as the export format). Admittedly, that's of little help if no other program imports that, but there is a real trade-off involved.

At least in Mendeley, I _do_ get file import when _unchecking_ the file option in Bibtex in Zotero, because that has Zotero include absolute paths in the .bib file.

What you can do and what I'd expect to work on all software (though who knows with Papers, which is hardly seeing any support anymore) is to replace the link to the file in the RIS (which is the easiest to work with) with an absolute paths using search and replace.
So say you've put the export in the C:/user/Documents
you'd do
search: L1 - file/
replace L1 - C:/user/Documents/file

I'd like this to work better, but it's not easy -- not least because what other software does with file imports is a black box. There no debug output, let alone code, where I could get a sense of what they're doing.

This worked like a charm. I tested on ReadCube.

Maybe a solution would be to give users a choice to export for other reference managers (absolute path) or for use by other Zotero (relative path).