I have an SSIS routine that reads from a very dynamic table and inserts whichever rows it finds into a table in a different database, before truncating the original source t
A option, that might sound stupid but it works, is to delete first and use the OUTPUT clause.

I created a simple control flow that populates a table for me.
IF EXISTS
(
SELECT 1 FROM sys.tables AS T WHERE T.name = 'DeleteFirst'
)
BEGIN
DROP TABLE dbo.DeleteFirst;
END
CREATE TABLE dbo.DeleteFirst
(
[name] sysname
);
INSERT INTO
dbo.DeleteFirst
SELECT
V.name
FROM
master.dbo.spt_values V
WHERE
V.name IS NOT NULL;

In my OLE DB Source, instead of using a SELECT, DELETE the data you want to go down the pipeline and OUTPUT the DELETED virtual table. Somethinng like
DELETE
DF
OUTPUT
DELETED.*
FROM
dbo.DeleteFirst AS DF;

It works, it works!