please try to understand that we aren’t speaking about software but about mathematics and physics.
If you just try to understand what happens in your essays you should be able to logically understand what’s the basic problem. Of course you get a lot of particles and it is absolutely clear why this is so. If it is still unclear to you, then please think purely logically. The problem is not linked to any kind of software but to the property of your image or the objects therein.
In your experience, do you have any recommendations for alternative software to obtain these parameters for the particle image in question?
There are highly advanced methods but I doubt they will help you much further with images of the kind you have provided. One such approach would be WEKA which is a pixel-based classifier that can be used for segmentation. But be aware of the fact that the more involved the methods, the more involved is their correct use!
As long as you have trouble to perfectly understand why your approaches fail, I’m not sure if I can full-heartedly recommend more involved methods.
If you are willing to follow a manual approach and draw a selection around your grain, then you can easily make all kinds of measurements ImageJ provides.