Not being able to get dimension texts to scale to sheet size, I decided to draw dimensions on each sheet, which may be a better practice anyway. But I ran into a bug (I believe) for which there is a relatively simple work-around.

When in sheet mode, I am able to dimension between ESnap points in model space, and when I do so with aligned, linear, or smart dimensions, the dimension displayed is the distance from model space. However, with continuous or baseline dimension, the distance displayed is the distance in the viewport.

The work-around, while it shouldn't be necessary, is pretty easy. Just highlight the dimensions that are on the wrong scale, and in the properties box, go down to the "Primary UnitSystem area, and change the "Dim scale linear" value from 1.0 to the inverse of your viewport scale.