I have tested the $140 SoftOrbits
RemoveLogoNow, and the result was unacceptably poor. I would not even accept the result if their asking price had been a hundred dollar lower!
You will get a better result the hard way, if you split each video into individual frames, one picture per frame, (at, say, 25 per second, that is a lot of pictures!!), and then run the $20 >
Batch Inpaint< from Teorex; it will do a much, much better job. But to finish, you will of course have to first merge the pictures into a video file again, and then sync the new video with the sound from the original video - which is why it is important that the 'split' is "per frame", not just some easier frequency. I don't know what program can do this split, for you.
All in all, you'll probably get the best result the easiest way, if you trial Adobe and Sony, and such.