Maybe you don't realise that the molecule you have drawn IS prodine!
See:
https://www.thevespiary.org/rhodium/Rhodium/pdf/prodine.pdf
for an interesting synthesis of this...
Looking in "Opioid Analgesics - Chemistry and Receptors" by Casy and Parfitt:
Page 252 contains a very similar diagram to the one you provided, they start with the 2nd compound you have pictured, then the arrow says "PhLi | (EtCO)2O" and the resulting compound is the same as the last molecule in your diagram with the methyl pointing both in and out.
The end product is referred to as "The original 3-methyl reversed esters derived from 1,3-dimethyl-4-piperidone" ... alpha-prodine and beta-prodine. It goes on to say alpha-prodine is equipotent to morphine, and beta-prodine is 5X morphine.
These 2 references are related:
L.O.Randall and G.Lehman, J. Pharmacol. Exp. Ther. 93, 314 (1948)
A.F.Casy in Guide to Molecular Pharmacology-toxicology, Part 1 (R.M.Featherstone, ed.), pg 217, Marcel Dekker, New York (1973)
On page 245 "Isoprodines (28), related to Beta-pethidine, are inactive in mice in doses up to 100mg/kg"
The molecule referred to by (28) looks exactly the same as the one you posted, except the Methyl is switched with the phenyl/OCOEt. The source is: M.A.Iorio, H.Michalek, and G.Damia, Chim. Therap. 2, 233 (1973)
Edit: Rhodium pretty much said what I said earlier and better, thats what I get for not hitting the "Submit Post" button for several hours...