Yes, it is possible for originals to work but CDRs to fail. They have different reflection properties which makes it more difficult to read them for a drive that isn't calibrated or is failing. It is true that Taiyo Yudens are better in this regard, but if the drive is so far gone, then it will eventually stop reading originals too.
A calibrated drive should be able to read all CDRs properly.
As you wish,but with not perfect media CD,you will always have doubt.
Every time I bought some unit that couldn't read CDs, or couldn't read burned CDs after modchipping, the problem was the drive not being calibrated - either the pot needed a minor tweak, or the tray needed readjusting. After that, they read everything fine. I had several Saturns that could even read cracked discs.
I burn any random disc; Verbatim, Sony, Phillips, whatever, they all work if the Saturn has a working drive. Taiyo Yuden only makes a difference if the drive is near dead or miscalibrated, in which case using more expensive CDRs only makes so much difference.
Also, Imgburn is known to cause bad burns without telling you so.
edit: and no, swap trick doesn't hurt the motor, you'd need to keep the motor held down for way longer than the window you have for swapping. It's always either the tray getting out of position, or the laser naturally degrading, but people always blame it on the motor.
I'd inspect the VDP2 and the VDP2 VRAM for any problems (broken pins, broken traces, any corruption), clean up that area of the board if it is dirty or dusty. If that doesn't help, reflow the solder of those pins with a heat gun.
Recapping will make the image more stable and the colours a bit sharper, that is if the system has problems with that. Note that if your goal is improving the image quality then you should also replace the EMI filters near the a/v output.
There is a status LED on the Rhea, it should blink once during power-up and then remain off. If the LED is lit, or starts blinking during gameplay, an internal error has occured. There are many possible causes of that, including SD card data transfer errors. The only way to restart correct operation of the device is to power-cycle the entire console. If the problem persists try a different card brand/size. If nothing else helps file a bug report.
IIRC Rhea only supports 32gb cards properly, anything beyond that is hit or miss depending on the card quality. I use a 64gb Kingston SD XC UHC-1 Class 10 card and did not get any problems yet.