"And we'll be free to make our own trade deals - each of which will include its own set of rules/regs/whatnots, along with a dispute-settling mechanism that is out of our control."
Now thats just a lack of understanding. To trade does not require we apply those standards at home. Whatever we export must meet the importers regs. We do not have to apply those rules here. So no leaving the EU to trade with the world is not the same as trading in the EU and being shackled by their rules.
"The notion that we can decide the nature of a two-sided border is just another of the unicorns the Brexiteers are farming."
That is another lack of understanding. A 2 sided border has (gonna shock you) 2 sides. We decide we dont want a border, we dont make one. Not our problem. If the EU wants one they can make one. The UK doesnt want a border, the EU does, its their problem not ours. No matter how many unicorns the EU want.