This sounds a lot like a hardware problem of something failing, rather than FreeBSD not being able to deal with some features enabled in the BIOS.
Have you tried a full pass or two of memtest? CPU fan(s) are OK?
I just had one machine that turned out to be a bad power supply: it would reboot randomly. (No kernel faults, no messages, just reboot as if the reset button was hit – Sometimes even in BIOS setup screen). Did you add the two NICs recently? Maybe their power draw pushes the board too close to the power margins.
regards, ....... Charlie