3.2: Numbers Upon Numbers

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Strangers kept surrounding Dorothy, mumbling cryptic strings of numbers...

"I'll see you in ten-two-fifty for five-eleven at one?"

"No, I have to drop by two-one-oh-eight by two to drop eighteen-one-hundred."

"Meet you in six-one-twenty for eight-oh-one-two, then?"

"In five. In six-one-twenty."

Below is a list of clues describing twenty-five strictly increasing three-digit numbers, between 001 and 999, inclusive. You will be able to place each number in the grid below based on its digits; although it might not be exactly clear in the middle, by the end there will be no ambiguities or empty cells. As an example, W has been placed for you.
     A: One-third of I
     B: Just some number
     C: A prime number
     D: The average of A, B, and M
     E: The sum of A and X, less T
     F: Another prime number
     G: The difference of Q and D
     H: The average of C, K, and M
     I: Thrice A                  
     J: The average of D and O
     K: The average of B and T
     L: The average of A and V
     M: The average of F and P                                  
     N: Twice D               
     O: The sum of D and E                                      
     P: Another pesky number  
     Q: A square number                                         
     R: Yet another prime number
     S: The average of H and X
     T: The sum of F and G
     U: The sum of C and N
     V: The sum of F and K
     W: Six hundred fifty-six
     X: The sum of B, E, and I
     Y: The sum of A, G, and L
6 7 8 9 0
5 6 5 6