Given I was having no issue on my right hand, I was hopeful that (with my right being my stronger hand) my left hand would build up some muscle and the problem would stop over time.
What did you do to try and build up muscle in that hand? It isn't going to happen just holding on the the hoods or bars.
While a majority seem to think that getting weight off of your hands is the magical solution, I don't.
A large bend in elbows helps absorb the road bumps that hands and shoulders would otherwise bear. Palms in a vertical plane along the sides of the hoods also helps.
Getting back to strengthening that hand, you'll need to do some real hand exercises. Not just hope that it strengthens itself while doing nothing. I've almost always found that strengthening the muscles around the part of my body that is annoying me helps with any pains I might have.