I would think that changing the recovery model to be bulk-logged immediately prior to the table loads then switching back to full would be the best option. Be sure to read up on things to consider (http://msdn.microsoft.com/en-us/library/ms190203.aspx) before implementation. This can be accomplished via ALTER DATABASE statements that could be added to the control flow of your SSIS package:
-- switch to bulk-logged mode
alter database <dbname,,> set recovery bulk_logged;
-- switch back to full
alter database <dbname,,> set recovery full;
Though I also have (and currently) relied on more frequent log backups to keep the log tamed, this is more art than science. Like most art, something's bound to surprise you; unfortunately, these surprises are more like a visit to the dentist: painful and probably preventable :).
I would also wonder if you're using the fast-load option on the oledb destination component (presuming that's what you're using). This should be minimally logging as well. There's a good white paper on numerous techniques for performance when loading data that might be worth checking out as well (be prepared, it's a doozey) . . . perhaps it can give you a few more ideas!