Have you tried speeding the record up (tried 45 rpm)? Does that noise also speed up?...Have you set up your turntable's anti-skating correctly?
@mzil: the rumble escalates at about that mark because I was performing a noise reduction in the beginning to try to isolate the offending sounds a bit better. The TT is a belt-driven Pro-Ject Debut III (USB) with a typical wall wart power supply. As the preamp is built into the table, I would not expect to be able to try the manual method you suggest.