Wow.... I've not read his book but...

At first sight, no Mauryan king are known to have struck coins with their name. Their coins were all punch-marked ones, in karshapana weight; so this argument is not.
And Devanam (piya) is not really equal to Sôter. Even if it was, we have two Diodotos, one Theos, the first, and one Sôter, his son. This is at least attested by the Euthydemos commemorative coinage.
And not refering to Diodotos... is it an argument? It's pretty uneasy to made argument ex silentio, especially when this Diodotos wasn't recognize by his greek neighbours like a king, just an usurper. We even must know the exact date of those Edicts referring to Greeks before beeing tempted to take this argument...