For what it's worth, any letters you send will first land on the desk of the judge's current clerk, and he'll probably only give a handful of them to the judge, so I wouldn't personally worry about offending the judges by applying to a lot of them since most of them will never see your application anyway.
On a similar note, and this is merely friendly advice which you can feel free to ignore, I would not recommend applying across the board at the trial level because a good deal of those judges will be talentless bozos. If I were in your shoes, I would dig up the contact info on trial lawyers in the area that you want to clerk in. If they're alumni, great. If they're your uncle's old college roommate, good enough. Worst case, if you have no connection, you could just blindly email public defenders or somesuch. Any competent lawyer that practices regularly in that court will know pretty well which judges are the good judges and which ones are less likely to be of help to you. State trial courts don't have much prestige, so you're going to really want to find a judge who people respect.
best of luck