Wow, kind of unreal post that one
1.36 - 1.39 dropping to 1.34 under load is called vdroop, most boards have it to a varying degree.
when you say you can't change it in the bios how did you try to change it?
Does your bios say "Please key in the values directly" or similar on the right side information pane when you click on the vcore setting?
Did you try using shift and + to raise the vcore? (and alternately the minus key to lower it)
Do you have any idea what you enabled/changed in the bios because it seems weird that the idle voltage has dropped yet the load voltage remains the same, sounds like it could be Intel Speed Step