I really can't picture this. Can you post a picture or a drawing?

For me, a backsplash is important on the sink wall to protect the wall -- but then, we are sloppy and splash a lot.

Behind the sink and faucet, a big rectangular piece of glass framed with a stainless steel molding will look nice. It will be self-contained. Also good behind the cooktop under the kitchen exhaust hood. Any other material, arranged as a framed rectangle, will look good.

This lets you have a washable wall protection which also defines a workplace spot and thereby adds interest. Without it, the space might feel a bit too undefined. And your wall may get grungy at those spots, over the long term. So you repaint. But the space feels undefined, loose and unfinished.

Any long thin backsplash causes the space definition problem which you have identified: "As a result the middle wall ... doesn't really have an "ending" on the far right side...."

A long thin backsplash surrounding the whole space causes other space definition problems.

It's all a matter of tradeoffs and compromises.

Yes, it physically needs a backsplash. How you design that backsplash and what material you use will be up to you. Sheet stainless is one choice to consider as it's easy to clean and unobtrusive visually.

krabbypatty, I am new to posting and I don't see a way to upload a picture. I have read the instructions but don't see the link that allows uploads on this forum.

We are messy too when it comes to clean up.