It is indeed a brilliant explanation, and if you read the link to Forvm Ancient Coins provided by Briac, you will discover who had this idea for the first time, namely Colin Kraay, in conversation with myself ca. 1972, when he and I were discussing such a overstruck As of Caracalla that the Oxford collection had just acquired.
Kraay never published his idea, but I have explained it numerous times in discussion groups online, in Harlan Berk catalogues, and also in Alfred De La Fe's online Journal of Ancient Numismatics. Briac knows about it because I explained it to him and other readers when he showed several of his own overstruck coins of Gordian III in the Forvm discussion group.
It is indeed difficult to establish what the undertype of your dupondius might have been!
Maybe P M TR P COS III S - C, Pax standing left holding branch and cornucopia, although this type is published only as an As, not a dupondius.
Indeed, dupondii with this reverse legend are very unusual. Cohen 1076 reports only a dupondius with type Ceres standing, citing Caroni's 1814 publication of the Wiczay collection. But this dupondius needs confirmation: Strack 673 found no specimens in the major and many minor European public and private collections ca. 1930.
Anyway, it seems doubtful that your coin can have shown this Ceres type, because Ceres holds a torch behind her descending right to the exergue line, and there is no trace of the bottom of this torch on your dupondius.