I don't mean to discourage you nor rain on your parade. I am a big believer on helping people achieve what they want, even if it seems like I am putting obstacles in your path.
I can tell you that about 20 years ago after quilting for 20 some years, I made a king sized log cabin for my cousin and was able to machine quilt a simple grid to hold it together on my vintage sewing machine. LOL I would not recommend the experience for a newer quilter.
My niece has requested a king sized quilt as a wedding gift -- I am thinking maybe I'd rather buy something expensive! I am much happier at dimensions less than 100".
You can look at some other block size options -- but sometimes Log Cabin quilts are best when square, depending on the overall design you want. If you took that pattern I linked and made a center color with 3 rows each side, it would make a 14.5 inch block, making 8 blocks per row would slightly decrease the size, to 116 instead of 120. Or don't underestimate the value of coordinating fabric borders!
Best of luck whatever you decide to do. Hope you work out your thoughts and plans with us here
