Right, I have now tried connecting my hard disk to the eSata port of the ExSys EX-3506 instead of its internal SATA port, and it unfortunately made no difference. (I did remember to put back the jumpers on the card to switch from internal channel 0 to eSata channel 0.)
UBoot seems to find SATA unit 0, but then just prints a number of dots until it times out and goes on to boot my next device (the SD card).
From Workbench, I cannot see the device either. Media Toolbox doesn't list the sii3114ide.device at all, and if I force it to check it by putting it in the tooltypes, it just says it cannot use it because there are no units attached (or somethnig like that). If I put sii3114ide.device into the tooltypes of Mounter and run that, it also finds no units.
I then tried replacing sii3114ide.device with the old beta sam3114ide.device Max sent me (which, as it turned out, I did already have, I had just put it somewhere where I didn't find it at first

), but that didn't make any difference.
So at least for the moment, it doesn't look like this card is a solution to the Sam460 connectivity limitations.
Best regards,
Niels
P.S. I forgot nexus' tip about trying with GiggleDisk; I'll try it and get back later, although I don't really have high hopes given the poor results so far.
nexus, do you have any other details about your setup which may make a difference? Is it exactly the same card which is working for you?