The further the UK diverges from EU rules, the harder it will be to trade across the two zones. That’s going to cause ambitious companies to leave for the massive opportunity in the EU, not to set up shop in the UK.
Likely outcome is that the UK will diverge barely at all in terms of the actual rules, but will rename a lot of things and give it all some sort of "Britishness" spit and polish, and most people who voted leave will be happy with it.
Customs controls need and are going to be imposed whenever there is no official agreement in place (and overseen by the ECJ) for regulatory alignment. And the ECJ oversight is a hard red-line for the UK.
Which means that it isn't a sliding scale. It's black or white. Either you fully align with oversight or you don't. And if you don't then you are hit with the full suite of custom controls.