I can't tell you about the best pick for YOU to use...but I can suggest a technique that has served me well...
Rotate the pick to use the more rounded edge...that's 2 out of 3. I play a Ric, and I've always found that turning the pic seems to mellow out the Ric click.
I'll second that emotion! I do the same thing with a Fender Medium 351-style pick. Sounds and feels really good on the flatwound strings I have on my P and Hofner Icon.