I have a couple stupid questions to help you diagnosis this issue.
1. Does the car have the MAF hooked up? I know with the ESS supercharger kits they get rid of the MAF but I am assuming it was put back in when they did the engine swap
2. Can you confirm that the car has the correct pre-cat o2 sensors? The e46 M3 uses a slighty different pre-cat 02 sensor then the Z4M. The first picture below is a Z4M precat 02 sensor is the second picture is a E46 M3 precat 02 sensor. As you can notice the connectors on the two sensors are completely different. If they used the engine wiring harness from the M3 they would have had to have used the M3 02 sensors. My only hesitation with saying this as a possible issues is I am not sure if the M3 engine harness would hook up to the Z4M DME. Now if the m3 engine harness does hook up to the z4 dme this could be why all your pre and post cat 02 sensors are getting faults and also your BSD line faults.
3. Has your shop tried to scope the BSD line fault? To me and dealing with these issues on a regular basis the BSD line fault might be the cause of all your issues. I believe on our cars the oil level sensor is on a BSD line.
4. Have you tried going to the dealer and asking them to flash the car with stock software? I think at this point you should try and make as many things stock as you possibly can to eliminate issues.
Edit: Forget #4.... just saw you tried this.