the only thing different about the inner third of the record is cartridge alignment accuracy becomes more critical, and possibly your tone arm, or arm bearing, has some mechanical interference or roughness over that part of the arc of travel.
your cartridge could be loose and the inner part of the arc could mechanically change the level of issue to create a resonance.
tt speed issues should not be arc dependent. rumble from the motor or bearing should be the same on the outer part of the arc the same as the inner part. is the arm and bearing smooth and free over the whole arc?
check alignment, azimuth and zenith at your inner null point. make sure your spindle to pivot distance is correct and you are using the correct template.