Depth plane and depthTestAgainstTerrain

The best workaround I can think of here is keep depthTestAgainstTerrain = true and use clipping planes to clip out a section of the globe that the tileset occupies, which is the 3rd workaround discussed in this thread: How to get more zoom level on 3D Tiles with Terrain

Instead of manually defining the clipping planes, you could generate them such that they roughly cover the bounding rectangle of your tileset. This code example may be helpful: