Struggling with component positioning. Am I approaching this incorrectly?

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I do a lot of signage and have been really struggling with getting components to align in a mathematical and precise way.
Say I have a component that is an extruded 45"X45" logo that is compromised of various letters, shapes, etc. I want to center this logo on a component that happens to be a 50"X50" board meaning I ideally have a 2.5" border on all (4) sides of the logo.
Just given how my logo is, when I go to create a rigid joint between the logo and the board I can't find a true center, since my extruded letters, shapes, etc are all off center which are the only things I can use to mount from my logo to the face of my board.
This then means I have a huge guessing game where I am messing with the offsets of my rigid joint and spending a lot of time measuring and adjusting.
I'm curious if there's a better way to find true centers for things like logos, organic shapes, or just any component that isn't perfectly symmetrical.
For all of the precision that Fusion has...I feel like what should be a 2 second process becomes a 5-10 minute ordeal.
I have developed a few work arounds for this (for instance I could sketch the 50"X50" board around the component, center it, extrude, etc). But these workarounds are only effective in particular situations. I
Thanks so much for all of your help and feedback and I apologize if this has been asked already, I looked around and could not find an answer to this.