I don't agree with the last point:
"why would a country be desperate to sign a trade deal with the UK, population 60 million GDP less than 3 trillion, when it wouldn't with the EU, population 450 million GDP 13 trillion?"
Negotiating a deal with the UK would involve aligning the interest of that country and the UK alone; difficult but not impossible. Negotiating a deal with the EU would involve aligning the interests of that country with 28 (once the UK has left) different EU member states and hoping that none of them derail the process along the way. For a description of what that's like you could ask Canada.
Countries will also want to make deals with the UK whilst it's desperate for trade wherever it can get it. The UK will either have to accept the shitty end of the stick in these trade talks or carry on getting slapped around with tariffs. In other words the UK has just volunteered to be the small kid that everyone else picks on in the playground.
Brexit means Fuxit.