holding a bird

Question
I remember a movie regarding fencing, the expert expounded that one holds the saber as you would a bird.  Too tight and you squish it, too loose and it flys away.  I have the same problem bowling. I am brand new to the sport, an accomplished technician and coach in another.  I have a custom fingertip drilled ball.  I either drop it early and it goes into the right gutter, or it sticks on my thumb and goes into the left gutter.  I scored 100 better with a house ball.  I know one should have more tension on the pads of their fingers than thumb.  I have also stopped trying to hook until I can stay out of the gutter, so we can rule out that ancillary funk.  I am 42, male, athletic, medium-small build, 15lb. ball.

Answer
First thing I would do is go to the pro shop to see if the span is correct for your hand. It may be that the span is too wide which causes less "grip" on your fingers. You may want to consider narrowing the span in order to get a better grip. It seems you have some problems with the thumb drilling. Perhaps the pitch of the thumb should be investigated.
Next if, on your backswing, you are holding the ball like a suitcase you might try holding your hand under the ball. This will help create a smoother release off your hand.
You can also curl your pinkie finger into your palm (most PBA players hold their ball this way). This naturally causes your ring finger to grip a little more to get a later release and/or more hook).
Another method is to try to "reach" for your mark while keeping your hand under the ball. This should cause your release to be a little later, almost like  you are "lobbing" the ball, to avoid dropping the ball.
I'm also assuming your use either the first or second arrow as your mark. Changing lines, to the third arrow, may give you more margin for error.