Hi,
When you activate the "floating tax prices" setting, it means that you enter the NET prices and that the customer will pay that price no matter the taxes calculated.
But in your last message, you seem to say that it's not what you want, and that you actually want the end price to vary based on the tax calculated.
In that case, you can't have floating tax prices. You need to have prices without tax entered in the products and have the tax added to these prices.
Now, updating the prices of all the products in one go will be easy with the mass actions system.
You just need to create a mass action with an action "update the values" on the column "price_value" with the mode "operation" selected and the value : price.price_value*100/120
When you process the mass action, it will update the prices of the products with that operation.
Note that thanks to the "Limitations" area of the mass action, it will by default only process the 500 first products. So you can process the mass action several times, each time incrementing the "start" field by the value in the "value" input field so that you'll cover all the products.
I don't recommend processing too much products at once as the process might crash because of your PHP limitations. 500 allows to run a mass action even on servers with important PHP limitations in place.
Note that if you process some products several times, you'll end up with wrong prices for them. So be careful. You might want to try that out on a copy of the website first.