I don't know why installing cedar horizontally would make it cup. Generally speaking, cedar is very stable. I certainly don't know everything though. :-)

Here's an article about cedar's stability

We saw a lot of the horizontal approach when visiting Toronto. The house we stayed in had what you are proposing with a verical stabilizer between posts. Looked very nice. We asked for quotes for horizontal fence for our back yard in central NY and couldn't get one.

If you search "horizontal cedar fence" on Houzz, there are lots of examples in photos posted by Pros.

I know- you just don’t see too many 7.5” wide fence boards. I can only assume that when a 5/8” board (which is what they are these days) is 7.5” wide it will be more likely to cup. I think I’m going to use truss head screws (w/ a pseudo washers) to keep it more stable. Currently search for those in stainless and all I can find are interior cabinet screws.

Grain, my back fence is very old and is as you describe. It was built of tongue and groove wood. Not sure if Cedar or Redwood. It appears as though a strenghtening board was first affixed to the panel in the middle and then the panel attached to the posts. The strenghtening board was cut at an angle on top. Mine is old and gray but it is something like this: