Your points are well taken and you obviously know more about Bradman than just about anyone around here
One of my points about (quality) pace bowling is that by and large it will trump batting.
Lara is a great but in 96/97 I see that his scores in Australia were 26,44,2,1,2,2,9,78,32. And I think that you can look at any (good/great) batsman and if they came up against a great set of fast bowlers their numbers do not look good.
Cook is a good batsman but in the 3 test series last year his scores were 115,0,24,46,7,3.
All I can say is that there is something freakish about Bradman's average that I think cannot be explained away by where he played his tests.