Do you have any overclock/undervolt running on your system? What happens if you remove xmp from your ram? Or maybe try to slightly downclock them to like 3000mhz and see what happens. Remove any overclock (if you have any from your rig also). If not, i don't care what microcenter says, it's definitely the card.
From there i'd suggest first downlclock the vram of the 3070 to the minimum and run a continous bench and raise the value of the ram little by little and see if at any point the blackscreen happens, same thing with the clock if nothing happens during the vram tryout. At that point, you'd know it's most definitely the card. And yeah tbh, i wouldn't trust a big chain like microcenter. Most often than not, they don't know wtf they're either doing or talking about. Why would they suggest a motherboard change to begin with when you can still hear the pc being active during the black screen lmao. Im sorry they made you spend money. Can't you take it to a smaller shop with actual people that know wtf they're doing? Or don't you have a friend/relative you can bring your 3070 to test on their rig?