I think that you can use the mt command to skip over the EOF mark. You would have to address the tape drive through the nonrewinding interface in /dev. For example, if your tape drive is addressed as /dev/st0 then there should also be another file named /dev/nst0. The first one will rewind the tape automatically after you perform a tape operation. The second one will leave the tape wherever it stops when you perform a tape operation.
So in summary you use the mt utility. The mt utility takes the fsf command to skip forward a certain number of files. You address the tape drive using the nonrewinding interface in /dev so that the tape will remain at the place that it stops when the mt fsf command is finished.
Code:
mt -f /dev/nst0 fsf 1
Then you can run your backup software as you normally would.
As far as removing the EOF I suppose you could record a meaningless value into that space on the tape. It might be a bit tricky. I don't know the exact length of the tape marks or what value would be good to write there. If you wanted to write one byte with the value zero you could do this.
Code:
dd if=/dev/zero of=/dev/st0 bs=1 count=1
I don't know if that would work or not. It might make things worse.