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1. It's hard to imagine that Safeco is going to affect Kotchman's BABiP very much, because as a, he hits a lot of ground balls and b, he's left handed. My guess is that most of the reason Safeco suppresses BABiP is right handed hitters hitting balls into left field that in most parks would be home runs, but at Safeco become lazy fly balls. Lefties get the short porch in right which is generally aided by the wind.
2. Looking at Fangraphs Batted ball splits, it looks like Kotchman's ground ball percentage went up in 2008, but down in 2009, admittedly still higher than his successful 2007, but, if you look at his splits page on fangraphs, you'll see something that should provoke hope that Casey changes his worm killing ways at Safeco. At home, since 2007, his ground ball rates have been: 52.2%, 56%, and 57.6%, whereas on the road, they've been: 49.3%, 49.2%, and 45.4%. Why? If you look at this articlehttp://www.hardballtimes.com/main/article/home-run-park-factor-a-new-app...
you'll see that Angel Stadium rates out as slightly below average for homeruns to Right, Turner Field significantly below average, and Fenway downright awful. Obviously these fields don't outright kill left handed pull hitters, but clearly Kotchman has limited power and he knows this, so my guess is that as he began to notice his batting practice cuts fall on the warning track, he adjusted his swing to not hit flyballs, on the road however, in parks that didn't necessarily supress right field homeruns, Casey let himself elevate pitches a bit more. The evidence shows up in his home/away splits, since 2007: 9 homeruns at home, 23 on the road. Since 2008: 4 at home, 17 on the road. If you look again at the stadium factors, Safeco grades out among the easiest to hit a homerun to right field, and I think Kotchman will take advantage of that.
3. I don't know where you get the idea that he's getting slower, he was caught advancing on the bases (on hits) once in 2009 compared to 4 times in '08 and 4 times in '07. And he hit into a double play on only 6.2% of his groundballs in '09 compared to 7% in '08 and 8.2% in '07. If anything, it looks like he may be getting faster.