After unsuccessfully trying the ATI Radeon Kernel-Modesetting driver with Linux 2.6.34, and reading about some performance comparisons with AMD/ATI's proprietary Catalyst drivers and the free Mesa DRI drivers, I decided to give AMD/ATI Catalyst (a.k.a. fglrx) another try.
When I decided to do that, fglrx 10.5 was in Debian's Testing, so I waited until the next day for fglrx 10.6 to enter Testing.
I've been using fglrx for the last 2:30 hours and haven't experienced any difficulties so far with OpenGL or Xv. Switching consoles works, suspend-to-RAM works, suspend-to-disk works, and I don't hear any buzzing from the screen, although I can't be very sure since the fan has been making very loud noises since around December last year. I have suddenly regained my faith in AMD.
There is one minor issue with Tux-On-Ice since it seems to run out of memory for drivers for the atomic copy step, probably due to fglrx. This causes TOI to try the same step twice or thrice before hibernating successfully — but solving this is most likely a matter of increasing CONFIG_TOI_DEFAULT_EXTRA_PAGES_ALLOWANCE (currently 2000) in the kernel config.
TuxOnIce debugging info:
- TuxOnIce core : 3.1.1.1
- Kernel Version : 2.6.34-bluecore280-suspend2
- Compiler vers. : 4.4
- Attempt number : 2
- Parameters : 0 667656 0 1 -2 5
- Overall expected compression percentage: 0.
- Compressor is 'lzf'.
Compressed 1638621184 bytes into 554865401 (66 percent compression).
- Block I/O active.
Used 78251 pages from swap on /dev/sda10.
- Max outstanding reads 851. Max writes 3700.
Memory_needed: 1024 x (4096 + 320 + 104) = 4628480 bytes.
Free mem throttle point reached 0.
- Swap Allocator enabled.
Swap available for image: 1496831 pages.
- I/O speed: Write 91 MB/s, Read 105 MB/s.
- Extra pages : 4118 used/4503.
- Result : Succeeded.
The Extra pages line is what matters here.
While performance overall is much better than with the open-source drivers from Mesa, and Frogatto is usable with Kwin's compositing at last — even if still slightly slower than in non-compositing mode — there are some occasional odd messages in the kernel's log.
[fglrx:firegl_acpi_video_event] *ERROR* Could not find private acpi context by video busid: LCD
Nothing to worry about, I hope. 
UPDATE: Effectively, increasing CONFIG_TOI_DEFAULT_EXTRA_PAGES_ALLOWANCE seems to have solved the hibernation issues.
- Extra pages : 4041 used/5200.