Cannot Connect to internal IP addresses
I hooked my laptop up to my WAP, which was a linksys router set to be "bridge-only" mode and should not be doing any actual routing.  With this, I was able to reach the internal IPs without issue.

So I rebooted the WAP and the problem cleared up.  I guess it had nothing to do with OSX/Apple after all, and just a bug in the linksys bridge-only code.