My old UV ran 3 springs just fine... some people have problems with it though so you'll have to experiment.
As far as your high string tension (causing the stiffness)... there are tons of causes...
Here are some of the obvious ones to check
-Truss rod relief (a pefectly straight neck
or an upward bow will cause heavy string tension... you want a slight bow for easy bending)
-Trem angle (maybe angle it forward a little - IE so the fine tuners are further away from the body rather than closer)
-Spring tension "trem play" - Dropping down to 3 springs will allow your trem to move more freely
I've amounted a ton of other theories on string tension but a lot are just for seriously anal-retentive fine tuning, and probably won't help you... stuff along the lines of pickup height
, neck joint angle/height, string composition... etc... Try the above, possibly with the help of a local guitar tech... and you should be good to go.
Also, the cotton ball idea should work for silencing your trem, unless you want to route the cavity a little deeper...