Do better job + V-ing

There is apparently no problem in distinguishing at least three possible meanings as made specific through context. However, I find no supporting evidence.

• 1/ choosing them to work with, 2/ as someone working with them, 3/ working with them rather than leaving everything up to them

(The apostrophe gives sentence stress)

• The people in group A have a better control than those in group B. So I am interested in people in group A, I can do a (')better job working with (')them! (either possibility of sentence stress seems meaningful)

• This teacher is not counselling his pupils well; I wouldn't have them do all these exercises; I can do a 'better job working with them!

• Having the task done by a subcontractor and giving up all initiative to their crew is not the best way to obtain good results: I can do a better job 'working with them!