I'm not sure you need to "just relax" ALL the time.
As a lifelong drummer, when I started playing the uke, I quickly learned that the same principals that applied to gripping the sticks a certain way also apply to the way I finger the fretboard or attack the strings. It all depends on the effect you are trying to achieve.
Certainly, when I'd sit up perfectly straight, straddle the drum stool, and attack the snare drum with my stick at a 45 degree angle, I would produce a much more forceful, robotic type of feel than when I sat back and let my sticks "dance" on the drums. On the uke, I find the instrument sounds completely different when I hug it to my chest, dig the finger nails of my left hand into the frets, and use short, firm strokes to produce a rhythm. This is often a desired effect, as opposed to the sweeter tone and feel created by gently cradling the instrument in my arms and brushing the tops of my finger nails across the strings.
I guess what I'm trying to say is that, maybe, keeping a tight grip on your guitar is not a "problem," but an element of your style. Perhaps, rather than being down on yourself for it, you just need to add "another" style to your bag of tricks!
Me with my first ukulele, a Junior Beatles model, in 1966. After Mom threw it down the stairs in a fit of rage, I became a drummer for life. At age 43, I bought my second uke...