I would not use western red cedar; it is weak and splintery and a person who grabs the trellis to keep their balance could break it. Using rift sawn or quarter sawn would not make a difference in this application. You still would have bowing issues.
What we did in the past for lattice and trellis work is to frame the panel with heavier material. Not just slightly wider, but thicker also. This gives your work strength and dimensional stability that the present design did not have. Using a frame of 1 1/2 X 1 1/2 would add great strength and stability. You could also make horizontal rails just above and below the circle that are smaller than the outside frame, but a little heavier than the other lattice pieces. This would give more strength and interest. Having the lattice members all one dimension makes it look cheap.
Here is some stuff from Roubo, note heavier framework:
Attachment 410564
Here is Roubo's
L'art du Treillageur, illustrations at the end of the book.
https://books.google.com/books?id=VQ...ardins&f=false