'Average' 1-10 Rolls on 2 D6

I asked a mathematician friend of mine to help us come up with a way to roll the numbers 1-10 on two 6-sided dice using custom numbers on each face of the two dice. We wanted the numbers to have a 'normal' distribution similar to the 2-12 rolls a pair of normal dice have only with outcomes from 1-10. My friend found two solutions for making a pair of 6-sided dice to have outcomes from 1-10 formed in a normal distribution.

Each 'Case' has 2 dice, A and B with sides as indicated:

          DICE                          Outcome Distribution
========================  =====================================
Case 1: A: 0 1 2 3 4 5    Number: 1  2  3  4  5  6  7  8  9  10    
        B: 1 2 3 3 4 5      Freq: 1  2  4  5  6  6  5  4  2  1

Case 2: A: 0 2 3 3 4 6    Number: 1  2  3  4  5  6  7  8  9  10
        B: 1 2 2 3 3 4      Freq: 1  2  3  5  7  7  5  3  2  1

My mathematician friends says that Case 1 fits true statistical 'normal' distribution for all positions within 3.76 percent. Case 2 fits as well at the ends (same dist for 1, 2, 9 & 10) but is 'skewed' towards the center values too much (about 15% off of 'normal' distribution). Both are useable for wargaming. Case 2 would be more 'average' in wargaming terms.

Die 1A's opposite faces would add up to 5, Die 1B 6, Die 2A 6 and Die 2B 5. As for the actual arrangement of the faces, that is left as an excersize for the reader. As long as the opposite sizes add up the the correct numbers statistical distribution should be 'fair'. FYI normal dice add up to 7 on each pair of opposite faces.

I'm posting this information for my friends who play Fire & Fury (both classic and regimental versions) as a possible house modification. FYI I tried this and locals universally hated it and much preferred the original 10-sided 'wild' dice.