I had the same problem with my brand new Surface 2, but for what it takes I partially SOLVED it doing this:
1) After Refresh/Reset and BSOD, keep pressing the Power button till S2 powers down. Press it again and the process will complete;
2) Do all the WIndows Updates, and reboot as necessary; your drivers will still be the August ones (not all of them, only the Tegra 4 ones), even if all the updates will be installed correctly;
3) Now, do a USB Recovery Partition Backup, info here:
Create a USB recovery drive for Microsoft Surface | Free up Surface storage space ;
4) Reboot your S2 with the USB drive inserted and keep pressing the Volume Down button till you see the circle spinning logo of Surface;
5) RESTORE your Surface from USB (when asked find your BitLocker key following the instructions and with a Smartphone or another Laptop/PC), choose to Repartition too, and if you see a message telling you to erase the Protected content or something like that choose Yes pressing the Volume Up button).
I had
no more BSOD after this process, even trying to Refresh/Restore normally from the HDD and not USB, so one problem is finally SOLVED for good.
But the Tegra 4 drivers will still be the August version...
Anyway my Surface 2 is still very stable, no glitches on screen, no lag, Halo Spartan Assault runs 60FPS without a single hiccup, and everything is butter smooth and stable.
My S2 only crashed once while in Standby and receiving a Skype call.
And I think that Tegra 4 drivers will be updated correctly on the next firmware update too.
This is a problem apparently affecting ALL S2 after Refresh/Reset, so taking it back to the Store for another one is a "non-solution"
Let's hope MS fix this ASAP, and not on the second Tuesday of January (01/14)...
Hope I helped!
UPDATE: I opened a topic on the official Surface 2 Community Forum too, here:
My Tegra 4 drivers won't update - Microsoft Community . If you have the same problems, please, post in there too and let our voice rise directly towards Microsoft!