I never came across those cases so I made a sling from mine.
Took a length of aluminium flat bar, drilled a hole to mount the recorder and a couple of holes at the top for the strap to clip to. I used a couple of keyrings through the holes then the clips from the strap clip to the rings. Glued a bit of rubber to be sandwiched between the recorder and mount and used a mounting screw I pulled out of an old monopod.
You really do need some way of slinging the device for it to be any use, especially if you are also booming.
First time out was a disaster as I was trying to stuff it in my pocket without tangling the cables and putting it out of record. Luckily I was shooting indoors and there was a table right next to where I was recording.