On a side, possibly related note, the SNMP on the remote box only works when I use the "Bind to LAN interface only" option. Is there any explanation about what exactly this option does and if it limits SNMP in any way?
it adds this to the snmpd config
agentaddress udp:161@1.1.1.1
where 1.1.1.1 is your LAN IP
otherwise there is no agentaddress statement.
There is an equivalent option for syslog that isn't configurable from the UI of m0n0wall. you could try kill syslogd and restart it with the same parameters and add the -b option with you local lan ip address and see does it solve the problem for you (most likely will), then maybe someone will code it into m0n0wall.