It seems the solution is pretty trivial, simply use the non-rewinding interface:
$ export TAPE=/dev/nst0
As seen here:
You seem to be using the device /dev/st0 which is a SCSI tape device. There is no problem with using that device, but it will always do a rewind after every completed access to that device. So after you have written a tar file to the device, it will do a rewind afterwards.
You wil need the device /dev/nst0. The "n" stands for no-rewind. After writing to that device, the tape position stays at the end of the tape. Try using the following commands:
mt -f /dev/nst0 rewind
tar cvf /dev/nst0 $HOME
mt -f /dev/nst0 status