Alright, final test to rule out firmware. This is the stock BIOS/SPI image from ASUS but with a cleaned/updated ME firmware as well (shouldn’t be needed in this case) after following [Guide] Clean Dumped Intel Engine (CS)ME/(CS)TXE Regions with Data Initialization. I suggest you flash with the programmer and verify afterwards that the reading result is the same before first power on (to check if the SPI chip is healthy). For good measure, clear CMOS, remove all power (AC + RTC battery) for 1 minute and swap memory modules. If the same problems are shown in MEInfo -verbose after that, you have a hardware problem somewhere and there is nothing more we can do on a firmware level.
Z97-A-ASUS-3503_clean.rar (5 MB)