Lindsay,
I had that happen to me not long ago. Same super informative error message.
What I finally figured out is that one of my domains (Excel autofill and overlooked by me) that I recently updated had been corrupted in my hosted feature layer.
I went into item details page for the HFS, data tab, fields. Then I would click on each field with a domain list on it, edit the list, delete one of the entries, and observe the "Save" button at the bottom.
If the save button becomes active, probably not the culprit, cancel and try next field. If the button stays greyed out, there is something wrong with that domain. Hit cancel and fix the domain (normally a duplicate in code or desc or both). Once I fixed this issue, export started working just fine again. (this also kept me from going the create replica route in REST as well).
In case this helps,
R_