It is interesting that the amplifier is still very close to the old 3458 design, even including the somewhat problematic inductor.
For the amplifier simulations the models often don't include variations between units and thus assume perfect matching between equal part. This can lead to a bit optimistic simulations. The measured performance is still impressive (in parts limited by the test system), though odd that the TL071 version outperformed the OPA1655 version.
With modern, relative fast precision OP-amps one should get away with 2 OP-amps in the integrator. It would mainly be with an AZ amplifier that the 3rd amplifier really makes sense. The version from J. Pickering should likely be OK without the AZ amplifier part. The OPA828 is also pretty good precision. The AZ amplifier at the integrator could be effected by the switching transients, despite of the filtering. The resistors in the filter add quite some noise.