Taxed based pricing from WebShop, Vertex

We have a webshop where unit prices are stored in the webshop incl. tax.

When receiving orders from webshop we frequently get rounding issues due to tax calculation.

Customers pay by credit card in the webshop. When shipment and invoice has been processed in E1, the invoice total is send from E1 to the webshop and invocie amount is deducted from card. However due to tax rounding the amount in Webshop does not always match the invoice amount.

To solve this issue we are thinking about implementing "Taxed Based Pricing" for the webshop customers.

Can we eliminate this rounding issue by using "Taxed based pricing" receiving the taxed amount from the webshop (total invoice amount incl. tax on the E1 invoice should equal sum of the entered "taxed amounts" on lines.