I've posted in the past, with some analysis, that the major difference in offensive production in the leagues is due to the DH vs. the pitcher hitting. So, I agree with you that the league difference in negligible......outside the rule difference.....but the rule difference will certainly have an impact on something like striking out.
For a quick comparison, using 2008 stats, pitchers and pinch hitters combined for 2846 K's in 9905 PA's. That's 3.48 PA/K. The DH struck out 1756 times in 9252 PA, for 5.26 PA/K. With a league average near 5 runs a game, you only need 4 LOB to average 5 PA a game, which is a nice round number I'll use to turn these rates into per game performance. The 5.26 becomes .95 K/G, the 3.48 is 1.43 K/G.
All other things being equal, ie the only difference in leagues is the rule difference, and the difference of 0.5 is really more like 1.0, or close to it, in terms of the ability to strike hitters out.
You know, if you want to credit the environment for the change, there's more to it than noting the change and the characteristics of the new place. An honest assessment would consider the original environment. From the 2006-2008, the HR park factor for Kaufman was .890. For Safeco, it was .930. There's more to it than just saying it's a park thing.