How can I accurately immitate this Picasa filter with Premiere's color correction filters?
This might be better suited as a comment to your original post, but alas I do not yet have those privilegies.

Anyway, my answer to you would be a cliché one: Keep tinkering.

It's really a matter of finding out what effects Premiere can offer, deciding which will be able to assist you the most and then going back and forth between them until you find a result that pleases you.

That said, you might want to check out the Color Balance effect. I find it very useful in most projects.