What got this project started was a really interesting part - a water bottle cage bracket that bolts onto the bike frame, and it happens to also fit the diameter of my handlebars - with just a bit of hand bending of the hinge to get it to open up enough to latch properly.
I coupled that with a 1" diameter rubber mounted zing ring clamp I found at Lowe's hardware store, which I then re-shaped and fit the squared off form. I knew I'd need some clearance to get the Polar watch mount high enough off of the handle bar top - to have enough spacing to pass the watch band underneath. I probably would have been fine with a 3/4" ring clamp, but I went with the largest one I could find to be safe.
The rest you can see in the photos. I added some #10 washers because I'm lazy. I figured it would take less turns to get the screws out when it came time to remove the watch. But the washers may be a PITA, so it may come down to finding hardware that's a better length next time I'm at the hardware store.
Ride with GPS just put a 'lock screen orientation' feature, which I really, really like. Unfortunately they place the landscape orientation 180 degrees out of alignment with what I need. So you betcha I'll be asking for a tweak to that setting, or will look for a customization that will force the orientation of the app at launch. (maybe an XPosed module?)
Anyway, if anyone else has a mind to do something similar, I think the water bottle clamp was $8, the ring clamp was $1.34 and the washers were $.38. So - $10 and you've got a workable solution that doesn't look too banged up.
[Oh - I've had that Polar watch mount forever, I think it's less than $10 too - so under $20 all-in would be a better estimate.]