I'm graduating in May of 2005 and I am also taking the lsat this October.
There was no possible way I could take the June lsat. Actually, I didn't even consider it. By taking the October lsat, you can devote your entire summer to prepping for the test, without finals and school stuff getting in the way. Although you will be studying somewhat in the Fall, hopefully by that point it will just be a matter of repetition of real lsats and you'll have the strategies down.
I'm not worried about the application process either. I'm planning on having everything done (applications, personal statement, LORs) by the time I take the lsat, so that once I get my score I can send everything out immedietely. I intend to make the Early Decision deadline for all of the schools I apply to as well.