that picks NTLM. Thanks to David Byron letting me test NTLM against his
servers, I could quickly repeat and fix the problem. It turned out to be:

When libcurl POSTs without knowing/using an authentication and it gets back a
list of types from which it picks NTLM, it needs to either continue sending
its data if it keeps the connection alive, or not send the data but close the
connection. Then do the first step in the NTLM auth. libcurl didn't send the
data nor close the connection but simply read the response-body and then sent
the first negotiation step. Which then failed miserably of course. The fixed
version forces a connection if there is more than 2000 bytes left to send.