Jim, the bungee on my sail was tight too - I think that the position of the hook over which it clips varies a little bit from boat to boat so on some boats the required stretch may be longer than on others. All I did was to cut off the 'stock' bungee and add a longer loop of my own.
If you do this you need a special bungee knot that won't slip because the stretch in bungee rope tends to work most normal sailing knots loose - I usually use a "simple simon" which is basically a reef knot with an extra wrap - this works well enough but a "vice versa" is probably better if you can find it (& then tie it right - I always struggle with this one which is another reason I tend to use the simple simon!).
I think that the bungee does 2 things -
1. it prevents the sail riding up on the mast by holding the sail canvas down at the tack - I am sure this has some effect on sail shape but, as you say, since the mast bends so much it is probably not as important as
2. it prevents the mast & sail falling out of the mastbase if you turn turtle. If you didn't use the bungee and then inverted completely the sail would still be connected to the boat by the sheet and IF you set up your sheet so that it couldn't slip through its blocks/padeyes you would then not lose the sail; the mast, however, could still slip out of the mast tube of the sail and would sink like a stone. Having turned turtle on a few occasions I always ensure that the sail bungee is secured when I raise the mast.
You may find it easier to pull the bungee down & over the hook if you do as I do & 'hotch' forward out of your seat to get a bit more leverage over it - stretching the bungee down any distance at arms length while bobbing about on an ocean wave can be a bit of a problem - your boat will be stable enough as long as you are a reasonably agile & well-balanced person