Yes, extrapolating is needed in this case to determine your actual allowable pressure.
From the Standard Pipe Code Table:
|Class, Temp 0F
||Working Pressure, by Class, psig
(225-200)/(300-200) = (X-5160)/(4660-5160)
X = 4785 psig is the Maximum Pressure Rating for 316SS at 2250F.
So that would satisfy your required designed condition.
Hope that helps.