Hopefully some one with access to a DEH KHODA DICTIONARY will check it and let us all know.
I had searched online for this before and never found it but NOW here it is: http://www.loghatnaameh.org/
Dehkhoda's Online Dictionary!
Here's a summary: Takavar's (تکاور) root means animals that can carry and run (horses, camels, etc) and used by Ferdowsi, Nezami, etc in their poetry as either 'fast or noble steed'. Today, ostensibly, it alludes to 'fast runner' although the entry isn't super clear to me because it still does break it up into 'tak' + 'avar'. Digging further, I don't see anywhere 'tak=attack' per se. 'tak' does mean, however, fast, active, intense, etc. Fascinating. (recall words like 'takapoo')
As for 'paa-tak' (پاتک), the search returns 'a new term' without further details. There is no entry at all for 'paad-tak' (which means little at this point).
So now we have developed a better hypothesis for what 'takavar' means: one who brings speed and endurance.
However, I don't believe this is the end of the story especially with 'paa-tak's' roots currently unresolved.