Where boxa and boxb are each connected to the router box with a crossover cable. The router box has the second network card in and working, but nothing plugged into it. So routing shouldn't enter into it. And no packets are being dropped, according to ifconfig. I am in the process of exploring all suggestions, and thank you all very much for the feedback.
Additional ideas are still quite welcome.
I confess I was hoping someone would just tell me to tweak a kernel setting, but I guess I'll keep plugging away.