Well if it was me, the fact that they didn't apply for a permit and that inspection wasnt done before boxing everything up, I would have them do the following and CC the city inspection department at the same time in all mail.

1) remove the drywall to expose the work done
2) while the drywall is open, have them run the line properly
3) get it approved by a licensed inspector
4) get them to close it all up

As for the spray foam idea, I'd have to wonder what the heat and cold cycles would do to that foam (I'm guessing it would eventually crack).

It's not your problem that the clowns tried to skip some steps.

Call someone for an estimate from another professional to fix it. That should tell you pretty quickly what kind of compensation you need.