How do you Convince the Oil Company when there is a Discrepancy in Calculations?

The Company is almost certainly relying on a Division Order Title Opinion that was prepared by a third party attorney. It is that third party attorney who needs to be convinced.

I wouldn’t sign a Division Order that I believed to be incorrect. You don’t say what State you are in, but in most, I don’t believe you are required to sign a Division Order to get paid. If you do ultimately prevail, they will have to pay you all the way back to Day 1.