1) Buy a new handlebar (not in my budget right now)
2) Build up a "sweet-spot" on my existing handlebars.
I decided on option #2 after seeing a few Instructables that used a product called Sugru - quote from their website "sugru is the new self-setting rubber for fixing, modifying and improving your stuff."
So I decided to give it a try.
Step 1: Materials
1 - Bicycle requiring handlebar customization - mine was a Specialized Tarmac road bike with Forte carbon fiber hardlebars
2 - Sugru - I needed Qty 2 - 0.7oz packets
3 - latex gloves - may not be needed, depends on if you think you may be sensitive to the Sugru
4 - scissors
5 - Handlebar Tape (optional - depends on the condition of your existing tape)
Step 2: Getting Started
Step 3: Filling the Gap
You'll notice there is a cable exiting along the side of the brake/shifter hood. In the picture of the right side, you can see a piece of red tape, it's used to hold that cable in place on the handlebar. It will keep the cable in place while the Sugru is applied and while it cures. And the tape is left in place while the new handlebar tape is applied over it.
Step 4: Tick-Tock - Waiting to Cure
Step 5: Finishing Up
I'm not going into the various methods and types of tape for wrapping handlebars, there are several good tutorials online, in fact here's a video, in two parts that I followed.
The Sugru in the gap did make for a bit of a challenge when re-wrapping that area, so you may want to use a more flexible type of tape..
You might also notice that the area seems a bit higher now than the part of the handlebar that curves toward the stem. The hood cover did end up with just a little wrinkle, but the broader area does make for a very comfortable place to rest my hands.
If I were to do this over, I might put just slightly less Sugru in the gap area, to take into account for the tape and the brake/shifter hood cover.