I am 6 years late to this discussion, but the topic is still a hot one. I am now immersed in the question of the script which the Pali Canon was first written in. I do not think it was Brahmi. Evidence of writing is so weak in India that despite the Brahmi script on the some of the southern Asokan pillars, it was probably merely a borrowed idea from the numerous inscripted pillars throughout the Achaemenid empire. In the north (Pakistan etc) the pillars are in Greek and Aramaic in the Karosthi script. And it is likely that many of the Greek immigrants and Greek bhikkhus could read and write fluently. There, the pillars made sense. There were many Greek (Yavana) monks in the area because of both the Persians settling them even before Alexander arrived in 330 BC. After Alexander, Greek settlements were abundant. These monks would have likely transcribed suttas and vinaya almost immediately upon hearing them recited, since they were literate and entirely familiar with book compilations.
Sri Lankan records such as the Mahavamsa, record Sri Lankan monks travelling to the Yavana area in the north of India to study with Greek buddhist scholars. They apparently had a reputation for Abhidhamma, as would be natural to literate monks.
The teacher of Bhikkhu Nagasena, of the the Questions of king Milinda,(the Greek king Menander,) was Dhammarakshita, a Greek abhidhamma master. He lived during the time of Asoka.
The Mahavamsa records the arrival of “30,000 Yavana bhikkhus” to the fourth council in Sri Lanka. This seems a wildly exaggerated number, but the event is certainly a large one. And now here is my theory. I think the Greek monks brought a fully transcribed copy of the Pali Canon to Sri Lanka. It was either in Greek script or Karosthi. The Greeks taught reading and writing to both Indian and Sri Lankan bhikkhus and left them to copy or write in any script available. Sinhalese script did not exist at the time, it evolved out of Brahmi apparently. The earliest written pali outside of the Asokan pillars are the birch bark scrolls from as early as 10 B.C. to 30 AD. They are in Karosthi script. They are very close in time to the so called writing of the Pali Canon at the Aluvihara in Sri Lanka. In fact they may be from that very time ( 30 BC).
One thing which is fairly certain: Greek monks were in the robes before Buddhism arrived in Sri Lanka. It seems that “western monks” are not a recent phenomena in Buddhism, but second after the Indian monks of the Buddha’s home area.
Now, Bhikkhu Sujato and Bhikkhu Brahmali are really the knowledgeable historians of early Buddhism so I leave these “theories” for their scrutiny and in fact would welcome any and all critiques of my conjectures. I doubt that the case can ever be proven, but I think it is plausible, unless I have overlooked some strong evidence to the contrary.