I'll try your tests, but I have a lot of problems to install distributions in the mmc, that is the reason I use external liveUSBs.
Today I tryed to install Deepin Linux, Linux Mint (Debian) and Sparky Linux. Deepin freezes while is copying files (I can not even move the mouse), and Mint throws me this message "Error 21 Is a directory: /target/usr/share/bug/udev" in the middle of installation. And Sparky Linux stopped and when I tryed to reboot it I got meessages like those:
mmc0: Timeout waiting for hardware interrupt
mmc0: Got data interrupt 0x02000000 even though no data operation was in progress.
mmc0: error -110 transfering data, sector 28833667, nr 5, cmd response 0x900, card status 0x0
Despite all this, I'm not 100% sure that the problem is the mmc, because today I've done a "dd" test in a pendrive and the system frozen too :-/