Hi Pete thanks for this file. I had a similar thought to you and put together a setup in Houdini. Your setup is a bit more clever than mine. Along the way I ran into some issues when uploading to the face tracking site that I thought might be worth mentioning for others going this route.
The first error on the site related to naming (this happens with your setup as well). My solution to this when exporting the fbx from Houdini is to keep the same hierarchy you get in Maya template file. To do this you need to define a name attribute for the parts and then on the ROP FBX Output you can turn on Build Hierarchy from Path Attribute and rename the attribute to name.
The second error I came across I couldnt solve in Houdini. The site gives the following error.
(Your mesh name) .... has an index buffer that doesn't match the expected index buffer. (the number of elements match). Possible issue may be the winding order of the polygon faces.
I did a match topology also and thought this would solve it. The point numbers do change so I was hopeful but it still generates the same winding error on the site. I tried various other options for changing the winding order in Houdini (clean, polydoctor) to no avail.
I then tried just bringing in the template.fbx and then exporting it back out of houdini as an fbx and this also generates the error. This leads me to believe that the Houdini fbx exporter is changing the winding order somewhere in the export process. If thats the case Im not sure how to solve this to have a houdini only solution.
After spending too long trying to solve it in Houdini, in the end I brought my wrapped mesh to Maya and blended from the validated mesh, this finally did get through the checks.