This is great advice. Thanks for offering it.
The company is small (sub 30 people) and I don't think they are acting in bad faith. I just went back with this:
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Hey <CEO>,
Thanks for getting me the paperwork and for working to accommodate my pre-existing condition (of being a <COUNTRY>ian)!
A little confused though? In my conversation with <CTO> I was offered full-time employment @ $XXX,XXX USD with benefits, vacation, and an equity package.
While I understand that it might not be possible to employ me as an FTE, I hope that we might be able to come to terms that are closer to what was originally offered.
I'm free after <TIME> if you'd like to chat!
<SIGN OFF> <PHONE>