welcome to the the forums Robert...
''I literally have zero router experience''...
we can help w/ that...
head over to this link for some light reading... (splines are covered there)
for other than the splines, I believe a router isn't the best tool for this project...
your cedar, is it Western Red Cedar??? It should be...
If I interpret what you doing you are actually making a vaulted arbor w/ a solid ceiling/roof... Correct???

your wood is going to have seasonal movement like it was trying to move it's self next door unless you select it carefully..

your staves..
I would use a splined (if the arch is self supporting) birdsmouth joint easily done on the table saw w/ a dado blade...

cut the spline groves w/ a slot cutter...
use white oak for the splines...

got more questions??? ask away!!!!