Turns out the Tabor MP440BX had several revisions. Mine is the 4000444. The 4000569 (or maybe 4000560) revision supported faster CPUs and more memory. I can't find any documentation saying it should take more memory, but saw forum threads where people had that board and tried the memory and it worked. Mine does have a memory controller that can handle the 256MB sticks, but the board itself won't.
I suspect that the hardware might actually be able to handle it, but the latest available BIOS update is dated 11/30/1999. Once the newer boards were out, they stopped updating the BIOS.