The local linear solve can return a worse step
The saved center Jacobians reproduce the failed right-side corrections almost exactly: the normalized step differences are below 2 × 10^-10. The center tangent therefore contains enough information to reproduce this failure; new native tangent capture is not the first required step.
For both starts, the bounded solver reports successful termination even though its proposed correction increases its own affine objective from approximately 2.444154 to 2.444221. Taking no step is feasible and has lower cost. This is a failure of that numerical solve on this narrowly bounded, poorly conditioned problem, before nonlinear aircraft propagation is considered.
Both center Jacobians have all 27 columns numerically retained, with condition ratios around 253 million. Removing only the timing correction for the diagnostic produces much smaller steps and reduces the affine cost. This does not justify fixing time in the scientific fit. It identifies the tiny timing interval and coupled calibration directions as the next numerical target.
The existing fresh native gate correctly rejects the bad steps: the subsequent position changes reach about 20 mm RMS per axis, above its 1 mm numerical limit. Those stopping limits should remain unchanged.
The next candidate should rescale the affine parameter box, preserve every physical direction and bound, and explicitly reject a proposed affine solution that is worse than a known feasible reference. Qualification needs known bounded optima and these exact saved systems. Success on linear systems alone cannot qualify the nonlinear archival comparison or change 51/0/2.