I see that you visited the post about my build. It is great to see how enthusiastic you are about building your own.
I measured my Y axis, it has been extended to 440mm or just over 17 inches. I did not modify anything in the supports, I just extended the rods, belts and base. The only difference is that i used XL Belt and Pully's as opposed to the MXL. They are just a bit bigger, my belts are 11mm wide which means I had to make other adjustments where the where rubbing against the structure.
And my reason for using XL, is that I could not source the MXL.
So I am sure that you will be fine with 18 inches.
Charles