This is the best solution that I've come up with so far to carry my Beastcage/phone. It keeps the lens and screen sides of the phone away from anything that could be abrasive, and provides room to carry accessories.
I have a Peak Design Everyday Sling that has a volume of 6L. Interior dimensions are 28x21x11cm (11x8.3x4.3"). It's shown in the images below, which are from a Peak Design video.
The design of the Sling includes the ability to add a Peak Design Capture Clip, which is the white object shown in the first image. This design feature is specific to Peak Design bags.
In the second image, note the white plate outlined in red. That's a small Arca Swiss plate screwed to the base of the camera. As shown in the third image, when you slide the plate into the Capture Clip, using any of the plate's four sides, the camera locks in place. The Clip holds the camera securely. Push a button on the Clip and you can easily slide the camera out of the Clip.
I discovered that if I screw the Arca Swiss plate to a 1/4"-20 on one of the long sides of my Beastcage, the Capture Clip will hold the Beastcage in an orientation that keeps the lens and screen sides of my phone clear of the Sling and my body. If whatever I'm doing requires it, I can position my hand on the bag side of my body to reinforce the separation.
I can place up to 6L of accessories in the bag itself, for example my light meter, neutral density filters, a miniature tripod or a MixPre and a microphone. Or some bottled water and a sandwich. I should note that Peak Design also makes a 10L version of this bag.
A Capture Clip can also be mounted on one's belt, but I think that a bag makes sense in this case and I haven't tried a belt yet. If using a belt, it's a good idea to get Peak Design's PROPad, which helps structurally and adds a bit of padding. A Capture Clip can also be used with a backpack strap. I'm bit scepical that a belt or backpack strap will work well with a Beastcage, but I was sceptical about the Sling bag too.

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