For posterity: It is not possible to include VAT in the price.
If I set the price to $2820.76 and apply the tax, the total will be 2990.01.
If I set the price to $2820.75 and apply the tax, the total will be 2989.99.
It is not possible to pick an intermediary price (changes that are < $0.01 are ignored).
The solution will be to use Stripe’s receipt handling.