The legacy back-end sits mainly on a MSSQL Server, with some data manipulation performed by asp pages on the IIS server
As a first step, it is possible to strip all business logic and processing from the SQL server, and extract to a module within Drupal.
The best way to do this might be to create a rest service which is capable of subscribing and unsubscribing users, and processing alerts.
Then a front end can be created to call the various endpoints of the REST service to query, add and remove subscriberse
Use Drupal as core.
Drupal content type manages the email subscription list
Drupal is used to render subscription forms etc as webpages on boston.gov
Cron in drupal manages communications dispatches.
Cron in drupal manages sync of Street sweeping (SAM) records and Street Occupancy (Hansen) records.
Use PostMark as the email delivery mechanism.
Retain Twillio for SMS (and voice?)
Use either existing MSSQL DB (COB Datacenter) or else port to MySQL (on Acquia)