I have made a number of Mariner's Compasses. I put the 4 segments together, then press like crazy and applique a whole circle onto the rays. I find it easier to pin a piece of muslin behind the opening and some of the rays, to stabilize the shape while I am pinning the circle in place. I also run a line of basting close to the edge and ease it somewhat before pinning and appliqueing.
I know that NYB is made in 4ths, but I think I would use the same general idea, since it is so easy to get something other than a true arc.
BTW, several years ago a friend with terminal cancer complained that he'd always wanted a compass, a pattern I'd never done. I made one with a somewhat wonky center, but he enjoyed it alot.