I've gotta say, I'm feeling pretty dense right now. On the General tab of the Job's properties in SQL Server Agent (still in Enterprise Manager), the owner was listed as:

DomainName\Administrator

which is how I'm logged into the server. I tried sa, and it still doesn't work. I appreciate your persistence, and by now you must be thinking "how stupid is this guy?".

rdjabarov: I'm using a mapped drive, which is the only way I've ever been able to get the FoxPro ODBC to work.