Continuously rasterized comp containing 2.5D elements gets offset and tiled when precomped

hmmm, precomps use the same toggle as Continuously Rasterize, but it is actually Collapse Transformations when they are involved.

For 2.5D comps, this allows you to build a house (for example) then bring this into a street comp.  A normal nested comp would then appear as a flat 2D layer, but when you collapse transformations, it acts as if the precomp is a 3D model (in effect).  I'm generalising and glossing over a lot of detail here.  I think your problems are that you are using the Faux Extrusion tools plus collapse plus 3D toggle.  You're probably confusing AE.

I don't think you need the 3D toggle, but I'd need to see your set up (any screenshots you can post would be helpful).  Another thing you could try is using Video Copilot's 3D Precomp script to generate linked cameras for each of your precomps.  Then, forget about using the collapse transformations tool entirely and just place them together.

https://www.videocopilot.net/blog/2014/08/free-script-3d-pre-compose-tutorial/