Graphics card related BSOD on startup - atikmdag.sys, dxgkrn1.sys

I have a Toshiba Satellite S50D-A that was given to me last August. It came with Win8 and between compatibility issues with my older software and Win8.1 turning it into a bread-warmer (running hot and largely useless) in December I downgraded it to Windows 7 Home Premium 64-Bit, making use of the Win7 drivers available from the Toshiba Europe support site.

Everything ran fine until about two weeks ago when it started BSoDing on startup, citing the atikmdag.sys file and Bugcheck116 in the BSoD screen and in system restores afterwards (not every startup, usually worked for several sleep/wake - restart - shut down/cold boot cycles before it F's up again, and seemed to most often come up on cold boots).

After trying a number of fixes listed online (such as manually expanding the atikmdag.sy_ file using expand.exe) I decided to backup all my data and reinstall the OS and all drivers from scratch. This has not, unfortunately, made the BSoDs go away.

As of my latest attempt at fixing it over the weekend, this is what I've done:
1) Clean reinstall of Win7 Home Premium 64 Bit, starting from a repartitioned, re-formatted hard drive
2) Installed all requisite Win7 drivers from the Toshiba EU support, including registry patches and double-checking that the BIOS is up to date, but excluding video card drivers
3) On the theory that it may have been a recent Windows update that messed things up, I made a system restore point then tried installing the Toshiba EU driver. It BSODed, I restored to teh save point and ran Display Driver Uninstaller to get back to a clean state
4) Ran Windows update iteratively until it ceased finding new updates
5) Installed a few pieces of software I most often use, that are not graphics card dependant (OpenOffice, Notepad++, Chrome, Calibre - I mostly use the laptop for reading/writing) so my system is at least useful in its driver-less state while I get the graphics problem sorted out
6) Explicitly created another clean restore point
7) Started with the AMD Drivers from the Toshiba EU site. Still continues to BSoD on startups - see the "EUDD" file attached
8) Gave up on the Toshiba EU AMD drivers and tried the following drivers from the AMD site:

• AMD Catalyst Display Driver for Embedded G-Series cards - Installed without problem, but video card shows up as a generic sVGA card instead of dual card setup. Ie, useless.
• Tried the AMD drivers for notebooks with HD Radeon series 8xxxM cards - did a full install of everything in installer package. BSoD on reboot but citing netbt.sys instead of atikmdag.sys (see "AMD Mobile" file) - possibly progress?
• Tried AMD's auto-detector tool. It came up with the same installer file as above. Did another reinstall, this time custom, and only installing the minimum of parts of the package. Got through several boots since yesterday and then it BSoDed again today, citing dxgkrn1.sys (see "AMD Mobile TakeTwo" file)

Note - between installs of the various drivers I restore to the save point, and run the Display Driver Uninstaller to make sure it's back to a clean state again, as well as manually checking C:\Windows\system32\drivers to be sure that all atikm*.sys files are gone

At this point I don't know what else to try, and whether I should be trying it with the Toshiba EU driver or the AMD Mobility driver.