I can't help you but in the 2000s they started to put copy protection on some audio CDs. Those CDs could not be played on cheap players or in car players that were using weird (and also cheap) hardware. Could that be the case here?
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I looked into this 2 years ago.
A portable CD player with bluetooth and SDcard exists.
The Monodeal CD707 seemed the most solid option.
Website is sold-out, but showing at 99 for a new unit on eBay.
3min review
https://www.youtube.com/watch?v=KWNy8MsdBZo
There are plenty of alternate models too.
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I'd initially be going for brands that make other quality, well known audio equipment like Fiio & Moondrop (Syitren also seems okay). Outside of that, I'd stay within my price range and make sure the player has CD, CD-R, CD-RW, MP3 and WMA capabilities. Like maybe the Klim Nomad portable CD player.
Also, just looked at the price of the Instant Disk - it's $270aud so you can for sure go the Fiio if that's your price range
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