Zoltan, these stats you sent:
        Session Duration:  7:06:49
        Object Inserted:   78,979
        Size of Objects:   2,480,911
        Idle Wait Time:    1:03:27
        Comm Wait Time:    3:39:06

say that number-of-files is the biggest issue.

Network speed isn't greate, but I see a lot of accounting log session
data, and 50% comm wait isn't abnormal.
Still, you can measure network speed like this:
        ftp  > put "|dd if=/dev/zero bs=200b count=1" /dev/null
to take TSM out of the picture.
If network throughput is still poor, take the results to your network folks.

About number-fo files: Multi-threading can help. It happens automatically
with recent clients (4.x? 3.7?) if you set the RESOURCEUTILIZATION
parameter high, like 10, and if there are
separate filesystems that can be processed at once.
Take this giant filesystem and split it up into several - perhaps using
symbolic links to hide that change from any applications.

Good luck.