A few points. Having owned a few Shuttle systems myself get a GPU with a blower cooler. It avoids loads of heat being recirculated into the case which can lead to issues down the line.
Also,Shuttle only tests reference cards and not aftermarkets which have different PCB lengths and cooler sizes.
Looking at the some of the cards you listed:
1.)HIS HD 6970 IceQ Turbo
Huge front fan housing will clash with the top of cage.
2.)Gainward GTX 570 Phantom 1280MB
Triple slot cooler.
3.)Gigabyte GTX 570 OC Windforce3X
Top of cooler with probably clash with cage.
4.)Palit GTX 570 SONIC Edition 1280MB
Cooler will recirculate hot air into the case.
The rest of the cards I assume are reference models, with blower coolers which will fit with a bit of adjustment in the case.