Hi Dustin,
The Cart doesn't currently support the ability to setup Shipping by Quantity and the postal code level. You can set up Custom Methods or Shipping Zones by Quantity but as you pointed out, this doesn't let you drill down to the Postal Code.
We are available to add the ability to the Cart. If you would like to be provided with a fixed quote to move this into programming, please submit a Quote Request at the following link -
Click here to submit a Quote
We quote all enhancements below cost since it is enhancing the module and in most cases we can start work within a week.
Thanks!