I’m a mechanical engineer who is (relearning Illustrator after many years away, and) a total newbie learning to create patterns.
The math calculation works for me as it easily makes sense in my head. Also, incidentally, my laptop operating system needs upgrading before I can load Photoshop and I haven’t gotten to that yet!
So for me - I can create a standard artboard called, say, “12in 300dpi export”, then I can set the artboard dimensions at 864 px square and I’m good to go. 

Thank you so much for this clear explanation and choice of fixes (I’ll try your other method, as well). I couldn’t for the life of me figure out why my JPEG file sizes were totally blowing out!
Typical Illustrator - exactly my experience of a couple decades ago as well; total fix for everything and also utterly non-intuitive. ;)