Grounding PCB to enclosure
Two solutions:


Include a shielded cable with the sensor. Put a sticker on the sensor saying: shielded cable is required.
Spend enough time to understand why your ADC readings are sensitive to the missing shield connection. Maybe you can improve this by changing the filtering on the signals on the inner conductors? 


For a product like this I have seen good results from connecting the board ground to the enclosure (not sure if you have done this, but I see no reason not to). 

Also I have seen this type of product with a full metal enclosure and only one shielded cable connecting to the outside being very immune to ESD and burst tests (CE) as well as very silent on EMI. So unless there is something I haven't picked up, you should worry if that is not the case.

Good luck.