How to calculate theoretical long-term projected savings for a DIY solar powered fridge?
You've ignored two major factors:

Batteries don't live forever, and require maintenance as well as periodic replacement - more so if they are abused (typical when people save money on batteries and then over-discharge them.) This is one reason that "grid-tied" solar is far more common where the grid is available - it eliminates the battery storage and its related costs and labor costs.

The second is harder for most people to grasp - if you paid the $19 dollars to run the fridge, and invested the rest of the $300, how much would that investment yield in 16.5 years? It's a little hard to know for certain since guaranteed bank interest is in the doldrums, but typical returns for sensible investments are near 5% - which would nearly pay your next year's power bill, and if there was any growth in the investment, you might end up making more per year than the power bill comes to.