From my research, ideal seating distance should be dependent on screen HEIGHT, not width nor diagonal size. Because it is dependent on our field of vision and the vertical axis is where our field of vision is the smallest. According to industry standards, the MAXIMUM screen size would be 2x the distance to the first row. The IDEAL seating distance will depend on the source. 3x for the SMPTE (Society of Motion Picture and Television Engineers), 2.89x for 20th Century Fox, and 2.4x for THX.
So pick your poison. But based on overall agreement, in your case you shouldn't exceed 72" of screen HEIGHT (12" of your first row seating distance divided by 2).
I chose my screen height based on the first row seating at THX recommended distance. 2.4x HEIGHT. In your case that would represent a 107"x60" screen. Which is a 122" screen. Just what you have calculated.
Don't forget that if you want to watch movies in widescreen format (2.40:1), your image will shrink significantly because you will give up the space occupied by the top and bottom bars. So on your 60" tall screen, your image may end up being 40" tall instead (effectively making the first row 3.6x screen height.
Getting a 2.40:1 screen keeps your maximum height fixed, but your screen becomes WIDER. Therefore bigger (144"x60").
Just something to consider...
I'm also in the process of building mine. And spending hrs and hrs researching these subjects. Really exciting. And wonderful folks in this forum.
Good luck to you!