Lets analyze logically.
When the data is big, the rate is high. But when the data is small, the rate is dropped. The difference between the two is, when the data is big, the request to the CMD is not busy compare to when the data is small. The request is only once or twice, then the data stream on to the Dat line. So the DAT line is okay, the CLK is okay, because when its transfer big data the rate is fast.
So i suspect the CMD line is noise, so there will be checksum, error, retry, checksum error, retry until it succeed, then when success the small packet goes to DAT line. And repeat again and again. This reduce the rate of data read from DAT line.
Here is my 1 cent suggestion:
1. Change the cable of the CMD with new one. Maybe the old cable problematic.
2. Try to clean the flux or any dirt around the CMD point.
3. In lite, the CMD point is directly goes to the emmc and cpu with some resistor paralleled to GND, you might check that resistor, it might broke.
View attachment 376193
If you use other device track it yourself in here
https://balika011.hu/switch/
4. Try to reduce little bit the resistance value. Use 33-40 ohms.