We just did a basement last week (for work) and also refinished our own basement recently - so speaking from some experience, I can say you won't be happy
in the long run patching someone else's job. You may save a few bucks now, you may even move before it hits you but IMO there is no better avenue than either to do it yourself or have someone do it properly the first time. You'll get more back right away...
The job we did for work had the same scenario: DIYer special with leaky vapour barrier and wobbly studs. All we were asked to do was reinsulate and correct the air leaks, since air leaks are more important than insulation levels. These guys had visible mould, so everything had to go.
But for our house, we did it correctly for up here: 2" extruded foam boards stuck directly to the concrete wall, taped and foamed, stud wall, 6mil plastic
VB and wall plugs sealed, and acoustic sealant used. Foam here and there. R20...
This is the state-of-the-art up here...and remember it is faster to put up your own stud wall (with foam underneath) with all your changes built in than to mess around with someone else's...in the long run. And as said, you can save 15% with the new federal HRTC.