I think that you are double counting. A dividend is a return of your investment. It does not provide Total Return because the stock exchanges reduce share price by the amount of the dividend on the ex-div date (as Joe alluded to).
IOW, if you have a 100 shares of a $100 stock worth $10,000 that pays a 4% annual dividend, on the ex-date you will have 100 shares of a $99 stock worth $9,900 and you are due $100 on the Payable Date. It's the same $10,000 either way, ignoring taxation if non sheltered. You can't have inflation ravage the $10k as well as the $100 or in the case of your example, ravage the $110k end of year one Total Return Value and the $1,000 dividend. It's already included
Where this gets complicated is that with dividend reinvesting, the prices at quarterly reinvestment will vary. OK, you assume constant share price growth and you make that linear to simplify. In addition, you have another complication with the compounding from dividend reinvestment.
The end result is that TR = Dividend + Return from compounding + Position appreciation and the total is 10%.
I'm not versed in the formulas for this so I'll not offer any solution. But FWIW, the following two web sites agree that $100k with a 4% dividend rate and 3% inflation would turn $100k into $106,796 after one year. The first one (Zacks) is the first part of the calculation that you used. The second gives a 10 year calculation of $192,999 which is less than your numbers: