When I input your values into the spreadsheet:
Inlet Diameter 11.8" (~300mm)
Orifice Diameter 0.5047" (~12.82mm)
Delta P 3.28 H2O" (~83.25 mm H2O")
I get a compressibility factor of ~ 0.99 and a Reynolds number of ~4.83 x 10^2. Even though the chart does not show a Beta value of 0.043 or Reynolds numbers that low, you can visualize that the curve tends to trend upward very quickly at low Reynolds numbers. So, from my graph you can't accurately determine a Cd.
Even when I input the 11.98 H2O" (~304 mm) I get a Reynolds number that is 9.42 x 10^2, which again does not show up on the chart and therefore you can't accurately determine the Cd.
These Reynolds numbers are really low, an indication of very slow moving laminer flow.
Can I ask, what CFM (l/min) flow rates are you trying to accurately predict?