If that helps as a data point, I was in a similar situation a few years back. Air France PE Ticket purchased on lastminute. Autocomplete gone wrong. I did not attempt a refund but a name change. Lastminute contacted almost immediately and promising a response within 72 hrs. Absolute hell ensued:
-LastMinute NEVER calling back as promised. Always me having to chase.
-Replied "you cant change the passenger to another person" multiple times, by a different person every single time, having to re-explain, having to chase up. Nobody keeping notes seemingly.
-Contacting Air France instead, whom after trying to fob me off back to lastminute, were very kind and listened to my story and exceptionally gave me the authorization to change the name (but I still needed to call OTA to reissue ticket).
-Calling lastminute again and being told to wait 72 hours, then being told "sorry you can't change change the person travelling" by a different person again. Having to re-explain to multiple people, nobody even trying to listen as per previously.
-3 weeks before the flight, desperately tagging up LM with a twitter message (my first tweet ever)
-getting a positive response within 48 hrs of the tweet.

Since you tried a refund I have no idea what will happen to you, but at least dealing with airlines seems to be easier than with cheap OTAs. If anything has to be learned from my fiasco it's to take it to twitter as soon as things go wrong.