I don't understand, why it is in all depth explained, how it doesn't work. Forget that "per bill" and all will work out.
No need for fixes, that "per bill" was not made for that purpose, that was for easy discounts on a bill.
Use "price modifier before tax". I tried that yesterday, working as expected. If you have the wrong prices showing up, use the prices configuration, there are close to ten different prices you can choose.