I don't know much about the history of the script, but I have a couple of observations:
1) The Kamarupa Kingdom, though based in Western Assam, also incorporated substantial parts of Bengal from time to time. I don't think there was any hard Bengal-Assam cultural boundary in those days. Arguably, even now it is hazy.
2) I don't know about ancient times, but I have seen 400-500 years old temple inscriptions from Bankura, South-Western Bengal. The script was quite similar to the modern one. One interesting letter form was that of "r" - the key letter where modern Assamese and Bengali scripts diverge. Guess what, it was written as a ব with a dot, BUT the dot is inside the triangle of the ব - clearly an intermediate between the two modern letter forms.
As for the second question: It's quite obvious that Bengali and Assamese have undergone divergent phonetic evolutions which have affected the letter values. More generally, it is an East-West thing. A lot of those so-called "Assamese" developments have also occurred in Eastern Bengali dialects. The divergence between the standard forms of Bengali and Assamese is magnified by the fact that standard Bengali comes from the South-Western extremity of the Bengal-Assam dialectscape, while standard Assamese comes from the extreme North-East. There's like 800 Km of distance between the two centres, as the crow flies.
