eWhisper, I did the same thing and it helped.
My most natural keyword AdGroup had 40 plus keywords (keyword phrases) in it. It got more clicks than any of my AdGroups but Broad Match killed it and it got only 10 - 20 percent of it's original clicks.
I tried using negatives and had over 100. The number of clicks still stunk, however.
So, I split it up as you described and clicks for those keywords rebounded to original levels. Having more targetted copy would explain part of the improvement but I think there's something else going on as well. (Google may have also been tweaking their Adwords algo at that time, which may account for some of the rebound.)
Overall, Broad Match cut my click 33% to 50% but now they're only down about 15% to 25%.
For me, CTR is up and the conversion rate has improved to a level I haven't seen for several months.
So, overall, I'm in the same ball park as before broad match.
Nevertheless, I need to become less dependent on Adwords for clicks since the handwriting is on the wall - "Clicks are only going to get more expensive".