Hello SOBX, welcome to the forum. I am not sure exactly how the wiring is set up in the 03 z71. But, the stock DVD player and stock center console should work the same no matter what head unit you are running. They just need to be wired in correctly.
For instance all electronics need to have a power and a ground. They also need a wire to transmit a signal to tell them what to do and when. For instance, the DVD player would need an audio, video, power, ground and a remote (the remote is a wired into anything keyed to the ignition... thus acting as a switch so you don't drain power from your battery when the car is not on). So, if your DVD playing has the correct outputs than all you need to do is make sure that the new head unit has those inputs. You can do this rather simply by removing the unit and looking at the back of them. If it is not clearly labeled on the back, take a sku # off of the back of the DVD player or control unit and check out the features on line.
If you are thinking this is a project you want to tackle on your own, I would love to help you out as much as I can. But, if you are still thinking you are going to take this into the guy for custom work, I would ask him for more information as to why this does not work. He could be saying that for many reasons, wants to sell you more products, has had troubles wiring factory DVD players to aftermarket head units on prior vehicles or different models and assumes the same to be true with this. He might already know what inputs and outputs all of these systems have and know that it would require highly labor intensive fix which might just be more cost effective to buy new and not worry about how the old stuff will integrate.
As always I am more than happy to answer any questions.