The wall was not prepped right and then they stuck the wallpaper over it.
Actually, it may have been okay for wallpaper. Truthfully, imo, it should have been better even for wall paper from what I can see. Humps usually do not6 show as bad with wallpaper. Paper usually has some kind of design on it that helps fool the eye where humps are concerned. Like when a ceiling is speced for popcorn texture, the finish does not have to be as smooth as it does for a painted ceiling. Sometimes it shows. This can depend on the lighting also.
Do you think he actually hung drywall or just tried to skip that process
Maybe, maybe not. Check around the door and window jams, and see if you can see any jam extensions to bring the jam out to the facing/trim. Might also check the electrical boxes to see if they have extensions. If the boxes are old work boxes with the clips that fit behind the rock to hold the boxes in, the same ones may have been used after the 1/4" was installed. I see no problem with just bringing these boxes out flush and retightening the clips.
If they were new work boxes (nailed to the studs), there may be extensions/mudrings on them to bring them flush with the rock. That or there may be 1/4" rock showing between the boxes and the covers, if he did not use extensions. Not cool.
the picture of the kitchen wall was putty coated according to his invoice
I thought one of the walls pictured looked like it had been skimmed. The old seams ( I think) should have been worked down some or feathered out more before he skimmed (puttied) the wall.
If he reinstalled new 1/4" rock over the old in the same orientation as the old with the thick seams, the hump would still be there. In other words, 1 seam with thick mud on top of another seam ( with more mud). From what I can see, it looks like the addition of the 1/4" may not have been necessary. I may have the pics confused, but it looks like one wall was hung horizontally, which may be code there. In that case, I think he should have worked on the old seams before covering with new rock. Either way, I would have worked on the old seams first by either widening the mud seam and feathering or removing some of the mud.
I removed the wallpaper and you could see the glue on the wall but the drywall was not damaged
He may have not wanted to deal with removing the glue residues which would have been necessary if he did cover it with new rock. Removing paper can be messy. May have been quicker for the buck to just cover it rather than having to make sure the glue residue was removed, prime (areas damaged down to the rock itself), mud and sand the walls smooth ,and skim coat.
You may want to see if he was licensed to do electrical work also, if he did that. May be a bargaining chip if he was not. Was the electrical inspected?
You are already out several dollars for an unsatisfactory job, might want to speak to an attorney that specializes in construction contracts. May not cost anything for a consultation.
Maybe check with the local Home Builder's Association. to see if they can recommend a good drywall company to at least come someone reputable to give a professional assessment of the situation for a reasonable fee.
You should be able to check your state's BBB for any complaints that may have been filed against this guy whether he is a member or not. I think he is thinking you will just let it go. Maybe some didn't and there will be complaints filed. More ammo.
Let me say, I am not a true professional drywall person, I paint. But I have worked in drywall and feel I have more knowledge and experience than the everyday home owner. Heheh, maybe more than some
of the people that work in it everyday. I really doubt that. Most of the people who have done it while pretty much know what is going on.
I am not there to see in them real time, but I feel I could have done a good job on the walls without having to install new board.
In fact, I have a before pic of a wall I skimmed that I intend to get an after pic of. When I do, I will post the pics if I can still remember how to post them.
Good luck! Keep us updated.