As far as I understood your initial requirements, you model a phoneme pose in the control rig… so you are adjusting various sliders until you get the desired expression.
Then I gues you want to animate the character to make these phonemes (make her talking).
The sliders in the control rig correspond to curve values that drive blendshapes. So you could create a pose asset with poses for all your phonemes, which in turn set the correct values for several of the blendshapes/morph targets. It’s not really creating a new blendshape stricly speaking, more like grouping sets of values, so you can control the single set.
For example your phoneme UE consist of the following values
CTRL_morphA 0.2223
CTRL_morphB 0.723
CTRL_morphC 0.21
You could create a pose “UE” for this. If your set the curve value for UE to 1, the character’s face make the UE expression.