I don't think that gripping down will change the swing weight much, however, it will certainly stiffen the club. If you are fighting a push or a slice, this will only add to the problem. My suggestion is to get fitted at a local pro shop, and they can suggest the proper length for your specific swing, stance, etc.

I personally think that choking down slightly gives me more control over the club, but it's mostly preference. If you choke down slightly and it feels comfortable and you hit them well, then go with it!

I'd put 1/2 masking tape, or some sort of tape on the grip and play gripped down for a while.  It will change things slightly, but only slightly.  Test the performance first.

RC

I'm also 5' 7" and have been testing the difference between 45" and 44.5" inch drivers.  One nice thing is the new 910 series where you can change out the shaft and test side by side the difference.  I find more solid contact and ability to stay in posture with the 44.5" but no lose in distance.  Follow RC's advice with your current driver or go test and get fitted for a new 910.