Your assumptions about exit pupil size and parallax error aren't correct.
Maximum parallax error doesn't depend on magnification. Objective diameter, focus distance and target distance are the variables in the equation to determine maximum parallax error (magnification isn't a factor).
Having said that, that's the equation for maximum parallax error. The amount of parallax error you will get (upto the maximum) for any given offset will be greater with higher magnification.
Not sure I've explained that very well, but the short answer is lower mag may reduce parallax error, but not for the reason you think it might.