Time Machine wants 16 days to do an initial backup. ps shows PRI = 33 with NI = 0. But I can not get sudo renice to set PRI less than 15. And renice sets NI directly with strange behavior for PRI. Any suggestions?

Question

Time Machine said it would take 16 days to do an initial backup, and indeed, after many days it is less than a quarter done.   (The problem started when I put in a new bank disk for Time Machine to write to for its backup file.)
Activity Monitor shows that the process name is   backups   with Process ID   6060.
Then putting this PID in Terminal UNIX command ps gave:
EdsMacPro-1:~ ed$ ps -l -p 6060
  UID   PID  PPID        F CPU PRI NI       SZ    RSS ...
    0  6060     1  1004004   0  33  0  2556488  29040 ...
Wow!  A priority of 33! 
Don't know how that happened, but the way to fix that (I thought) is with renice. 
But renice doesn't work.
After a lot of playing with renice and ps, it looks as though renice can not make the priority better than (no less than) 15.
And the parameter you put in, that according to the man page that is supposed to be priority, turns out to be "nice index", with priority changed by sometimes subtracting or sometimes adding either this number or twice this number - down to a limit of priority no less than 15.
EdsMacPro-1:~ ed$ ps -l -p 6060
  UID   PID  PPID        F CPU PRI NI       SZ    RSS ...
    0  6060     1  1004004   0  33  0  2556488  29040 ...
EdsMacPro-1:~ ed$ sudo renice 5 -p 6060
EdsMacPro-1:~ ed$ ps -l -p 6060
  UID   PID  PPID        F CPU PRI NI       SZ    RSS  ...
    0  6060     1  1004004   0  28  5  2555964  29028  ...
EdsMacPro-1:~ ed$ sudo renice -5 -p 6060
EdsMacPro-1:~ ed$ ps -l -p 6060
  UID   PID  PPID        F CPU PRI NI       SZ    RSS  ...
    0  6060     1  1004004   0  38 -5  2555964  29028  ...
EdsMacPro-1:~ ed$ sudo renice -15 -p 6060
EdsMacPro-1:~ ed$ ps -l -p 6060
  UID   PID  PPID        F CPU PRI NI       SZ    RSS  ...
    0  6060     1  1004004   0  48 -15  2555964  29028 ...
EdsMacPro-1:~ ed$ ps -l -p 6060
  UID   PID  PPID        F CPU PRI NI       SZ    RSS  ...
    0  6060     1  1004004   0  48 -15  2555964  29028 ...
EdsMacPro-1:~ ed$ sudo renice -n -5 -p 6060
EdsMacPro-1:~ ed$ ps -l -p 6060
  UID   PID  PPID        F CPU PRI NI       SZ    RSS  ...
    0  6060     1  1004004   0  53 -20  2555964  29028 ...
EdsMacPro-1:~ ed$
This is with OSX 10.7.5 and Terminal 2.2.3 on an early 2009 Mac Pro with lots of memory.
What am I dong wrong, and any suggestions for how to fix my Time Machine process?

Answer 1

The backup file size is 1.67 TB.*
That's across the internal bus of a 2009 quad-core Mac Pro - which is pretty fast.
Copying an hour's worth of MPEG-2 HD takes about a minute.
I do a fresh backup from scratch about once a year, and the last time it finished over night.
This time the first Time Machine backup is only about 1/5 complete after many days, and Activity Monitor shows essentially no use of disk drives or of CPU.  And in the first note I pointed out what is gleaned by using Terminal to execute the UNIX ps command. The priority of the running Time Machine process looks incorrect to me. 
I could be wrong, but I think the problem is process priority, not file size.
I am unable to set priority to 0 or a negative number.  Can someone straighten me out on how to do that?
[*The machine has four 1.5 TB disk drives in it plus lots of memory.  Two of the physical drives are configured as one 3 TB backup drive (RAID concatanated).]