Could the fact that the light source is not an absolute point source cause a slightly too large reading which is more readily apparent in large aperture binoculars?
It not only can, but necessarily will. Whether the effect is big enough to account for your discrepancy is another matter. It depends largely on how far away from the objective you measure the outgoing light cone.
Think for a moment about what's going on. If the binoculars are focused for infinity, then a perfectly collimated cylinder of light entering the eyepiece will cause another perfectly collimated cylinder of light to exit the objective. If the outgoing light is a cylinder, then it doesn't matter where you measure it, and it's physically impossible for it to be bigger than the objective.
But in real life, this can never be realized, for three reasons. First, it's impossible to focus perfectly for infinity. Second, the light source isn't at infinity, so the light hitting the eyepiece is actually a diverging cone. Finally, the light source isn't a point, so the incoming light is actually a *converging* cone of *diverging* cones. (Draw a picture to understand what I mean -- I don't want to take the time now.)
All of these effects result in the outgoing light being a diverging cone -- and one with rather complex geometry. So the farther from the objective you measure it, the bigger it will be.
However, I still suspect that error of measurement dominates all of those effects combined. Honest, it's really pretty hard to measure a light cylinder or cone accurate to 1 mm.