Your experience is not unusual, given the chipset and driver of your card, plus that it's in a PCI-E slot doesn't help either. Does your Tyan board have an Intel chipset, such as an ICH10 or ICH9, used on most Intel socket 775 or 1366 boards? If so, you could move one or more of your 320's to the Intel SATA interface, and the Tool Box should work fine. That is likely your only option, besides moving them to a PC with an Intel chipset board and doing it there.
The Tool Box has been known to work on some AMD chipsets, but not on the Marvell or NVIDIA AFAIK.
The Tool Box firmware update won't work if you have drives in a RAID array even on the Intel chipset and driver. I believe it will on a single drive not part of an array on the Intel chipset.
Thanks for the confirmation that the ICH controller is the only one to attempt.
I was worried as I had assumed that the three mini-sas ports on this board were all tied to the LSI controller. Having to undo all the cabling in this 1U just for an update would have been a bit of a pain. Turns out one is tied to the ICH10 controller and just moving one cable let me update with no fuss.
I'll also go ahead and note that I used unetbootin to make a bootable USB stick for this, that worked very well (choose FreeDOS "distribution" and then pick the intel upgrade iso).