We need to see the actual query code, not just a very brief summary of what the code contains, as well as full table and index definitions. You wrote: "Here's what the INSERT looks like", but that code doesn't even include an INSERT!
The recovery model of the source db is irrelevant.
The destination db log file should be expanded to the size needed for the load before the load begins. This prevents dynamic expansion of the log, which can be a very slow operation.
It would also be very helpful to have the result of this command:
EXEC [destination_db].sys.sp_helpfile
And, to make sure the log file is not too fragmented, the number of rows of output from this command (NOT the result themselves, just the total number of rows listed:
USE destination_db;
DBCC LOGINFO;