Metformin reaction mechanism #Kani

Recalled a chat with Eugen about metformin synthesis may have an equilibrium between the dimethylamine hydrochloride and the free dimethylamine, the latter which attacks the dimethylformamide. Reaction mechanims drawn out. So, maybe water as a solvent and adding base would push the equilibrium to the right-hand-side, favouring the free base?

Next wondered whether dicyandiamide would be water soluble.... https://thechemco.com/chemical/dicyandiamide/ suggests so, and also states that dicyandiamide is a strong base. Therefore, this might be sufficient to remove the proton from the salt forming the free base. Alternative mechanism drawn.