Personal opinion - you may have an easier time blending between morphs if you have the jaw as its own actor (using a ghost bone) and localize your morphs.

 In terms of modeling - model the mouth with a little bit of an opening for easier selection. Then use whatever app you prefer to create your morphs.  For the cartoon characters, one of the reasons you can turn on all their expressions at the same time and still get something useable is because I localized my morphs to key areas and then combined them via dependencies to create the expressions. Would love it if we could have weight mapped translations - right now only rotations are weight mapped. Then I could do some higher end stuff but anyway, what app you make it in doesn't matter as much as your approach.

 One major factor to making this easy is that we separate the teeth, gums and tounge from the head geometry now.  Similar approach to what is often done in animated films. So then you can create a obj of your figure that is just the head or just the body for easier morphing. I usually import the figure into zbrush, isolate the internal bits - teeth, eyes, gums, tongue and delete them. Then I save the file out as "Character name-FBM".  I will then select the head, inverse the selection, delete and save the head out as "Character name-Base Head".  

Hope that helped.