Well, I checked the calculations I had been shown and I couldn't find anything wrong with them.
And do you think that this indicates that the calculations are solid or that you are crap at maths?
I'm willing to bet that your calculations assumed the mass of the CSM totaled about 30,000 kg.
Then you would lose that bet. We don't need to assume anything about the mass of the CM. Not when we have the actual numbers at our fingertips.
Did you account for the fact that the CM mass is not a constant?
Bear in mind, if the CSM wasn't going to the Moon and back, there wouldn't be need for anything like the full load of propellant.
Which would require all of the ground crews to be in on it. And their support teams. And their suppliers. And their support crews. And their accounts department. And so forth. You are fast approaching the inevitable conclusion of this train of thought if such it can be described. Everyone is in on it except you.
I believe it was Ryan Mackey who formulated the Expansion Hypothesis of Conspiracy Theories whereby as the hoax claims continue, the required number of co-conspirators grows exponentially.
Also, something was added to reduce the acceleration of the S-IVB. After all, you don't want it smashing into the back of the CSM. When you have worked out what was added, do your calculations again.
Actually, two things were added to the S-!VB. Forethought and planning. Most here are familiar with the steps taken to avoid collision. But you are not. Why?