Now that the long dd command is running, it is too late to redirect its output. Maybe you are far from the console and you cannot use screen or to create a FIFO for its stderr...
... but you can still use two ssh session and strace !
On the first ssh session you can write
sudo strace -ewrite -p `pgrep ^dd` 2>&1 | grep -v "write(1,"
On the second instead (read the warning note below for the signal to use -SIGUSR1 or SIGINFO)
kill -USR1 $(pgrep ^dd)
And read a not so nice output from the first similar to the one below
Process 26176 attached
--- SIGUSR1 {si_signo=SIGUSR1, si_code=SI_USER, si_pid=29517, si_uid=0} ---
write(2, "329094980+0 records in\n329094979"..., 47) = 47
write(2, "168496629248 bytes (168 GB) copi"..., 34) = 34
write(2, ", 109.221 s, 1.5 GB/s\n", 22) = 22
Note: Unfortunately (even if differently reported) the command kill -USR1 $(pgrep ^dd) will force the running dd processes to write to their original stderr. For this it was needed to modify the original answer (you can see in the version history).
Warning: As reported on this other answer the signal to send with kill instead of -USR1 may depend from the Linux distro. Under OpenBSD -SIGINFO under Ubuntu SIGUSR1. Check it carefully in advance a wrong one can terminate the process !