Check to make sure your right crank arm is properly attached to the bottom bracket and then make sure it is torqued to the proper specs. I would also recommend checking to make sure the bottom bracket is adjusted properly. It could be that the increased pressure on the cranks when you are on an incline are exacerbating a right crank arm or bottom bracket issue. Its worth checking out.
if you open the shifter you may find it nearly impossible to put back together as they are not designed for easy overhaul.
On another note:
I don't agree with your shop mechanic (based on your previouse post you referenced) that STI wont shift chainrings when on an incline but this second round of postings seem to have you neglecting or rejecting sound advice given to you by multiple forum members. It is a bit counter intuitive to shift to the big ring while climbing...though not totally unheard of. In order to do so effectively one usually has to lighten the pressure they are putting on the pedals as the chain/drivetrain is under more tension when climbing. If you have applied this change in technique but are still having the problem then definately check your bottom bracket and crankarms as I suggest at the top of this post. If these things don't work then you need to go back to your shop and tell them they are full of ****e and talk to the owner about replacing your defective drive train.
-j