I spent a few more hours googling and foudnfound the appropriate support document on Red Hat's site: https://access.redhat.com/solutions/53031
It turns out Red Hat 6+ will filter asymmetrically routed packets by default.
The solution is to To make this behaviour persistent across reboots, modify /etc/sysctl.conf and make the following change prior to reboot:
net.ipv4.conf.default.rp_filter = 2