But is the Cessna 172 series certified for spinning other than an incipient spin only?
Some certainly are, read the flight manual. An "N" model I once operated was certified for spins in the utility category but with two heavies on board and a bit of fuel you were outside of this. Not a very convincing spin trainer either, took effort to induce a proper spin and simply letting go of the controls, it would recover to a dive instantly that took height and some g force to correct.
Not something I would recommend in an old 172 ...