Network connectivity trouble to non-routing multi-homed hosts?

Question

I have two networks: A and B (172.16.2.0/24 and 172.17.2.0/24). A is Ethernet, B is WiFi. An OpenWRT router connects A and B, and most traffic gets passed OK. Default route on router leads to a cable modem on the Ethernet, and traffic to the Internet works fine.

I have two multi-homed Linux machines with both Ethernet and WiFi interfaces. ip_forward is set to 1, but the machines do not normally perform routing (they are not listed as anybody's default gateway).

A WiFi-only machine can ping any WiFi address, and can ping any Ethernet-only machine's address, but cannot ping the Ethernet address of either of the multi-homed machines. (They can ping the router's Ethernet address.)

Pinging a multi-homed host's Ethernet address while watching with tcpdump shows ICMP request packets arriving from WiFi to the multi-homed Ethernet address, but no replies being sent.

Multi-homed hosts can ping any other host, but by default those pings go out on the interface attached to the destination's network.

Ping from the multi-homed host using the "-I [ethernet-address]" option results in ping packets going to the WiFi host, and properly-addressed replies coming back, but the ping process never receives them -- it says "request timeout."

The multi-homed hosts are Ubuntu and Debian; no iptables rules in use and the default policies are all ACCEPT.

Any idea what could be gobbling up packets from [WiFi-addr] to [Multi-home-Ethernet-Addr]?

[Added info per commenter's request:]

root@vegas:~# ip a
1: lo:  mtu 16436 qdisc noqueue state UNKNOWN 
    link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00
    inet 127.0.0.1/8 scope host lo
    inet6 ::1/128 scope host 
       valid_lft forever preferred_lft forever
2: eth0:  mtu 1500 qdisc pfifo_fast state UP qlen 1000
    link/ether d0:27:88:d5:72:7b brd ff:ff:ff:ff:ff:ff
    inet 172.16.2.250/24 brd 172.16.2.255 scope global eth0
    inet6 fe80::d227:88ff:fed5:727b/64 scope link 
       valid_lft forever preferred_lft forever
3: wlan0:  mtu 1500 qdisc mq state UP qlen 1000
    link/ether 9c:4e:36:01:64:2c brd ff:ff:ff:ff:ff:ff
    inet 172.17.2.250/24 brd 172.17.2.255 scope global wlan0
    inet6 fe80::9e4e:36ff:fe01:642c/64 scope link 
       valid_lft forever preferred_lft forever
4: tun0:  mtu 1500 qdisc pfifo_fast state UNKNOWN qlen 100
    link/none 
    inet 172.19.0.1 peer 172.19.0.2/32 scope global tun0
root@vegas:~# ip ro sh
default via 172.16.2.254 dev eth0 
172.16.2.0/24 dev eth0  proto kernel  scope link  src 172.16.2.250 
172.17.2.0/24 dev wlan0  proto kernel  scope link  src 172.17.2.250 
172.19.0.0/24 via 172.19.0.2 dev tun0 
172.19.0.2 dev tun0  proto kernel  scope link  src 172.19.0.1 
root@vegas:~# ip ru sh
0:  from all lookup local 
32766:  from all lookup main 
32767:  from all lookup default