Hmm. Well, on one hand I guess it's a nice surprise to see that ExFAT is now being used in these devices instead of the rather antiquated FAT32. My apologies for sending you on a wild goose chase with that one.
I completely agree that the write speed of that card should not be an issue at all even with 4 channels of 24/96. Data rate of a 2-channel 24/96 recording is 4.39Mbit/s - that's mega
bit, and your card is rated 40 mega
byte / s so it shouldn't be an issue at all. I'm beginning to think you have a bad card. I have had genuine SanDisk cards go bad before. If you have this issue with other cards though, it could be an issue with the unit.
The only SD cards I have right now are Transcend class 10s, which are definitely not "approved", but I have perfect performance with them for photo and video.
The approved card list for the 70D is extremely short so far - I'm hoping they get around to testing more cards (scroll to the bottom):
http://tascam.com/product/dr-70d/specifications/