>In all practicality, the UK will have a brief moment in time where it gets to do as it wishes with the VAT structure
The UK only has control of it's internal regimen - there will be no (UK) VAT paid on sales into Europe (no more EC Sales/Reverse Charge Mechanism) in future but VAT will be paid on all consumer imports at least - businesses will offset against UK VAT due. It's not immediately clear how the HMRC will make up for the billions in VAT it stands to lose, but they have published advice:
(if you think negotiation was a tad flakey - look away now)
https://www.gov.uk/government/publications/vat-for-businesses-if-theres-no-brexit-deal/vat-for-businesses-if-theres-no-brexit-deal