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From Guth's book, "The Inflationary Universe," 1997, at page 182, he mentions that photons were around before 300K years after the BB, but they were being scattered by plasma. After 300K years, when there was enough cooling for hydrogen atoms to form, the photons were free to travel in straight lines. In a footnote on the next page he says this:

According to the big bang theory, the separation between points A and B [in a diagram] grew from zero to 90 million light-years during a time interval of only 300,000 years. The rate of separation, therefore, was much larger than the speed of light. For a subtle reason, however, this does not violate the stricture on faster-than-light travel. The complication stems from the fact that, in general relativity, space itself is plastic, capable of bending and stretching. In the big bang theory, the space stretches as the universe expands. The restriction on velocities remains valid, in the sense that no particle can ever win a race with a light beam. Nonetheless, the distance between two particles can increase due to the stretching of the space between them, and general relativity places no restriction on how fast the stretching can occur.

Nonetheless, the distance between two particles can increase due to the stretching of the space between them, and general relativity places no restriction on how fast the stretching can occur.

Yes. That's what I vaguely remembered. Another way of putting it is to think of it as not as a case of photons speeding up per se, but of the photons being displaced by the spatial inflation. They, along with the matter, are just going along for the ride. Measured in a local frame of reference, nothing was physically breaking the cosmic speed limit.

It's an almost lawyerly explanation to get out of a cosmic speeding ticket, doncha think?

Guth is not very clear in that passage. The "inflationary phase" doesn't last for 300,000 years. According to this useful timeline, the universe was 21 orders of magnitude older at the time of electroweak symmetry breaking than it was at the end of inflation, and 23 orders of magnitude older at the time of radiation decoupling than it was at the time of electroweak symmetry breaking. Most of the expansion happened in an exceedingly brief time.