First, it looks like your selling estimate after 16 years is reasonable - a $300,000 selling price less a 6 percent commission and some selling expenses would net you around $275,000. That would mean around a 2 percent compound annual increase in the value of the house.
Here's how I would look at your two scenarios.
Scenario 1
You pay OUT $44k in the down payment, $151k in principal and interest payments, and $80,000 to your savings account, for a total outflow of $275,000. At the end of the 16 years, you get BACK $171,000 in net house equity plus your savings of $80,000 (ignoring interest), for a total of $251,000. You lost money.
Scenario 2
You pay OUT $44k in the down payment, $227k in principal and interest, and $3,600 to your savings account (3 x $1,200). The total out is $274,600. At the end of 16 years, you get BACK $275,000 in house equity and $3,600 in savings (ignoring interest), for a total of $278,600. You are slightly ahead.
I think you have incorporated a sign error in thinking about the amount in the savings account. Your cash flows to the savings account are going OUT of your pocket and into the bank account. The money comes BACK to you at the end of the 16 years, just like the equity in the house does. Does this make sense now?