If the problem is the two hour downtime window while you back up the files, you might:
1. Move the files elsewhere on the same disk/array.
Provided you dont cross onto another disk, the move should be almost immediate. Requires diskspace. After the move, you should be able to restart the process that writes to these files, with just a few minutes of lag. You back up the moved files.
2. Rename the files
The files remain in the same spot, but have a different name.
You can rename the files. Requires diskspace. After the move, you should be able to restart the process that writes to these files, with just a few minutes of lag. You back up the renamed files.
3. Archive the files before backing them up
If these large files can be compressed, you may gain both time in backing them up, and you'll use less tape, for a double savings. Be sure to choose a good archiving program.