Hello,
I understand that you are referring to "ideal" gyrators that can reverse an impedance without introducing additional unwanted elements, e. g. series resistance, provided the non-ideal amplifier properties can be ignored so far.
If so, the single amplifier circuits must be excluded from consideration. Alternative "ideal" two amplifier circuits can be found in literature. The question could be regarding advantages of different solutions. The presented circuit has minimum part count, don't know if alternative "4 auxilary R" circuits exist. Another circuit from a popular german electronics textbook allows for a ground referenced Z2 but needs 7 auxilary R.
Do you think that the presented circuit has inherent limitations that could be possibly avoided in a different approach? What should be exactly the circuit with reversed OP polarity? The last time, I built a Gyrator circuit was about 35 year ago.
Regards,
Frank