You can configure an extended event session with an event:
error_reported: This event gets fired every time that an error happens in the server.
For your particular case you are able to filter events for message_id = 248.
SELECT text FROM sys.messages WHERE message_id = 248
The conversion of the %ls value '%.*ls' overflowed an int column.
That event ...
So, I am attempting to find out how to use XEvents to see the exact INSERT/UPDATE statement that the error is really occurring in
You should be able to capture desired activity by configuring extended event session with following events:
rpc_starting - Occurs when a remote procedure call has started
rpc_completed - Occurs when a remote procedure call ...
Take a look at slave_type_conversions parameter in your parameter group on the replica. There's an option to allow truncation due to data type difference between master and replica. Please note this is a static parameter, so it will require a reboot of the RDS instance to take effect.
First, the error seems something wrong with login (as per following query)
select * from sys.messages
where language_id = 1033 and message_id = 18456
When you told to simply rename DB Name in connectionstring, did you verify which username was used, and the same username exists as login with appropriate permissions on SQL server, you can verify this via ...