First - you should be aware that Tymoczko's usage here is not standard. The term fauxbourdon is usually only used to refer to the late Medieval/early Renaissance technique of almost pervasively harmonizing in this manner. This is all before tonal harmony, and fauxbourdon can be employed in any mode, though care needs to be taken to use B-flat or B as necessary (or musica ficta in the earliest appearances) to avoid tritones. That said, I could guess correctly what he meant before reading the link.
The example that comes to my mind - a little later than what you're looking for - is the minor variation in the 2nd movement of Beethoven's Kreutzer Sonata. It begins with parallel 1st inversion triads as 16th notes over a C pedal. This first looks like a series of passing tones over a V7 chord, but in measure 4 we get a #iiidim65 - iv6 progression, followed by i6 - flatii6 - V7 - i in measures 5-8. The last four measures have a completely different harmonization in all the major variations.