... (lots of calculations)
Final Comparison
Variance of 20d6: 58.33458.334
Variance of 1d20+1d12+53: 45.166745.1667
The variance of 1d20+1d12+53 is closer to 58.334 than previous combinations and represents a reasonable approximation for both mean and variance.[Edit: Just checked it in google sheets, this looks right to me]