Hello Will,
I've run into some odd numbers on the checkout screen when implementing the VAT rules in hotcakes back-end.
From your doc's it states that the product prices should include the VAT amount, and the store will reverse-engineer the values based on the tax schedule's added into the back-end.
I've tested this on the website we're having problems with that has some customizations to the checkout page & a clean hotcakes install on a separate DNN instance just to rule out any customizations interfering with the hotcakes VAT rules.
I've entered in a product with a price of $100. Setup a tax schedule of 10% and applied it to my product. On checkout I would expect to see the product total to be $100, where the 10% would be deducted from the $100 so the item's price would be $90 and the VAT tax $10.
On the checkout screen it's showing me $110 for the total so it looks like its doing an addition instead of subtraction. I've tested with VAT on/off but the calculation looks the same regardless of VAT being on or off. It's looks like VAT on is only adding an additional line item to the checkout summary.