Seems like it might be a good plan to do a test trip or two beforehand someplace where you can dump tanks at will, even if not a full hookup site. That is a good idea too just from the point of view of getting acquainted with the rig and its systems. A nearby state or corps of engineers park might do the trick very nicely without a huge expenditure of cash--or even camping in your own driveway, especially if your house has a sewer cleanout access within reach of your driveway that you can hook the motorhome up to.
Often the gray water tank tends to fill more rapidly than the black water tank.