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Yeah I also saw your comment above after I posted mine as well.
That's the downside of non real time commenting..

I think the disk has a problem with popping side ways or upwards
when we angle the phone backwards too much,,
It reaches a point where the circle disk seems to loose traction with the slot and will pop out.

You can test this by rotating all the way backwards..
With the weight of the phone and it being rotated all the way backwards, it will cause the disk to lift and pop out.

Maybe there also needs to be a bump on the disk so it can't rotate back too much..

Good idea about printing the disk a bit bigger..
It will be a bit more tighter..
Probably try to test it at 103-105%


Also an idea for you..
If you like logo/branding on your work..

Consider doing a small simple logo like
-a simple logo picture / shape
-your Initials designed as logo etc..


Using an entire email as a logo/branding
-is too long
-does not look as nice on the prints
-also some printers don't print lettering very good so it makes the print look less nice.
-small simple logos that are unobtrusive..and looks artistic looks much better than an email address