Well, your years of study are worth much more than my idle speculation, so after browsing your paper I'll happily accept that you're right.

But my intuition is that the instructions themselves executed under such a masking system are no more able to perform timing attacks on the rest of the process than arbitrary code from one process can perform timing attacks on another.

If there's something specific I'm missing there I'd love to know what it is so I can update my mental model.