Question about the operation of a zener for a rapid relay release
You don't want the catch diode (D2) if you want rapid relay release.

As you surmised, the catch diode keeps current circulating within the relay coil while it decays.  This current flow keeps the relay pulled in until the current decays down to the relays' release value.

By removing the catch diode, you allow the coil voltage to rise.  When you clamp that voltage spike to a much higher voltage, the current decreases by the same ratio.  The current decays down past the relays' release current much faster.

I'm glad that you posted this question - it made me go back to your earlier question and I realized that I had missed seeing the catch diode (D2).  I have modified my answer to that question to mention removing it.