So, here's how it plays out.
In the OLE DB data flow source, rather than using "table or view" as the Data access mode, you have to set it as SQL command. Then you must wrap the field in a CAST() function to cast the field as varbinary.
SELECT CAST(funny_field AS VARBINARY(254))
I learned that in Foxpro, 254 is the largest field width you can have for a varbinary.
I haven't tried converting the varbinary data into character data before inserting into SQL Server yet, but once the varbinary data is in SQL Server, casting the varbinary back to varchar in a select seems to work.
SELECT CONVERT(varchar(255), funny_field)
On a side note, selecting the results to grid gives the impression that the data is still being truncated, but selecting the results to text will display the character string, FYI.
Thanks Jack, for the tip on converting in the source.