If you decided to use Boeings or Airbus Optimized V-speed philosophies you will find that you are using improved climb most of the time.
For the more generally used Boeing method of balanced field calculations, you should already have the ability to reduce your takeoff thrust using Fixed Derates and an extended environmental envelope up to 69C. This should provide you with approx a 35% thrust reduction.
Before you initiate an improved climb policy to enhance engine savings, I would ask your engine manufacturer to quantify the savings associated with getting the full 35% thrust reduction.
IMHO I believe that you will find that crews hate higher V1 speeds but will not be too concerned about increasing the speed margins above VMC and the climb gradient.
Mutt.