Hi Maria.
Thank you for caring so much about my problem. I value this very much.

I just tried 3 different USB cables (excluding the one I initially used), but none of them made any difference.
I tried with different ports. Unplugging all other USB devices, including my USB harddisk, my Kensington Turbomouse (trackball), using Apple's mouse again, etc.. Unfortunately, there's no difference yet.
I then decided to finally open my TINY-H (as it's now more than 2 years old) and check if there was any loose connections, but I spotted no visible errors so far.
After a lot of struggling with USB cables, wrong assumptions about OpenOCD, uninitialized variables, possible driver-errors, I decided to try something completely insane.
I have this very expensive switch-mode 5V DC power supply.
Now I found a good old heavy +6V DC power supply and used this one instead. I'm not afraid of burning off the board, because I checked the schematic, and it should at least, as far as I can tell, be able to handle voltages above 13V.
After using this heavy (6V, 2A) power supply with enough juice, I tried the "reset halt" command.
No timeout.
"reset init"
no timeout.
-So what you're experiencing with the one USB cable for power and another USB cable for programming might be this:
Your power cable must be short, in order to work, otherwise the voltage drop will be juuust big enough to get below what the board requires.
Try measuring this, if you have equipment suitable for it.
So whenever people have problems with these timeouts, ask them if they have at least 6V DC on the power plug.
When I read the printing on the board (which is partly hidden by a screw), I can now see that
it says 6V, not 5V, like I first read it as.
-So this is an "error 40", eg. my own fault.
...But I hope it helps you as well, in catching problems related to too low voltages.
Just tried running my flash-script...
source [find interface/olimex-arm-usb-tiny-h.cfg]
source [find project.cfg]
adapter_khz 15000
proc program_sam7 () {
# halt the processor:
halt
wait_halt
# write file to flash memory:
arm7_9 dcc_downloads enable
sleep 10
poll
flash probe 0
flash write_image erase unlock "MyBlinker0.bin" 0x00100000
sleep 10
# start execution of the program just downloaded
reset run
sleep 10
# exit OpenOCD:
shutdown
}
init
reset init
program_sam7 ()
And something very
strange happened.. I have two LEDs blinking on the board.

I almost can't believe it works. Thank you for all the help you've provided. I know that if I just switched the power supply, I would probably have said "That's not it, it still doesn't work", and I'd have switched back to using the old PSU again.
But I'm really grateful that my config files are correct now. I still have the 'Warn' line, and it's most likely related to a config file, but I guess it doesn't mean that there will be any serious errors with flashing.
Love
Jens