@ Nuts
I can see "trimming" to a CAS/AoA, but not a mach or TAS. For a small altitude delta, the TAS or mach would not vary much. I only flew 2 jets that had a "mach hold" using otto ( F-102A and F-101B) , otherwise we humans had to maintain the mach for our climbs or level flight. In my 1800 hours +/- in straight-wing jets with no otto, I never noticed the phugoid once I had the sucker trimmed. Well, maybe +/- 50 feet and 1 or 2 knots until I had the thing nailed.
I saw your neat graphic for the phugoid, but seems the condition for the model was thrust equals drag. So my question is, "what happens when thrust is greater than drag", especially for a go-around that should have been executed in the incident? I would have preferred a graph of unrestricted FPA using the configuration and commanded gee/AoA.
As with others here, I think the phugoid considerations for the 'bus FCS had negligible effects upon the incident. However, I was surprised that the jet even had some phugoid elements to the laws. Always learning, ain't we?