Thank you for helping me find the answer in the documentation.
Should anyone else ever read this post, here is some additional useful information:
GridLineHorizontalOffset and GridLineVerticalOffset are properties of the DiagramPage class. DiagramView contains a property whose implementation is DiagramPage, but the property casts the DiagramPage to Panel before returning it. Therefore, in order to access the unique properties of DiagramPage, you must cast the DiagramView.Page property.
Here is the code that worked for me. Note that diagramView1 is a pre-existing reference to the relevant DiagramView:
var diagramPage = diagramView1.Page as DiagramPage;
diagramPage.GridHorizontalOffset = 12;
diagramPage.GridVerticalOffset = 12;
The documentation for DiagramPage.GridHorizontalOffset and .GridVerticalOffset contains code examples to a similar effect.