After much weeping and nashing of teeth I decided to punt and try a different motherboard. After putting the MegaRAID card and the SATA drives into the new motherboard everything worked flawlessly.
My configuration is now:
Gigabyte 8IEXP w/ P4-2.26
1GB RAM
LSI MegaRAID 150-6
6xWD 250GB SATA in RAID 5
So my issues appear to be from the MegaRAID card conflicting with the P3 motherboards which both have VIA Apollo Pro133A chipsets and not NASLite. The 8IEXP only has 32-bit PCI slots and the MegaRAID card works fine.
I just need to upgrade my network from 100-BaseT to Gigabit and I'll be set!
-ScottH