Thanks for the input!
When my device is plugged into a 1.1 port, the application appropriately recognizes the device and appropriately recognizes its speed. Unfortunately, the actual protocol is too large for the packet size of 1.1 HID. To support it, I would have to implement a way of chopping protocol packets up over multiple USB packets and re-assemble on either side. Do-able, but non-trivial. The resulting data-rate isn't unusably bad, but it is a noticeable degradation.
I haven't found any southbridges since 2003 that didn't support high-speed, but I have found that AMD southbridges usually have two 1.1 ports. I think the pain threshold would be finding a chipset that supports the rest of the application (>XP SP2 and SSE3) but doesn't have any high-speed support.