Desiging for Dot-Perfect Diagrams: Advice?

I create a lot of math diagrams for the Monarch. It is sometimes important for certain lines to be thicker than others. However, the thickness at which the lines display varies depending on the graphic’s position relative to the Monarch’s pins, and even the thinnest lines can display as two rows of dots. Right now, the only way I know of solving this issue is to cross my fingers and nudge the graphic around little by little until it displays properly.

My question is this: Is there a way for me to predict which pins my graphic will display on before I open it on the Monarch? I would like to create a sort of dot grid template in my drawing program so that I can control how things will align. I know the tactile viewer sizes images based on the size of one braille dot, but I don’t know how to use this information or measure it accurately. I use 24.35pt Swell Braille.