Entonces puedes usar SQL dinámico como este...
DECLARE
@Fields nvarchar(Max),
@SQL nvarchar(Max);
SELECT
@Fields = COALESCE(@Fields + ',', '') + column_name
FROM
information_schema.columns
WHERE
table_schema = 'dbo' AND
table_name = 'Instance' AND
column_name <> 'PrimaryKeyID' --here you exclude columns
ORDER BY
ordinal_position;
SET @SQL = 'INSERT INTO dbo.Instance'
+ ' ('
+ @Fields
+ ') SELECT '
+ ' ('
+ @Fields
+ ') FROM Template;'
EXECUTE sp_executesql @SQL;