I feel like the answer to this is going to be a *facepalm* moment for me, but here goes...
So I realized today that I was unable to use rcon to make in-game modifications to settings.  Sending any commands after rcon_password mypasswordgoeshere would result in a response that the server was not found at 192.168.0.100:27015 (the LAN IP of the server and port number).  I read some HL2 forums stating that for some odd reason on Linux, you have to specify +ip 192.168.0.100 in your command line or script.
Sooo, I did exactly that...rcon works now, but the server no longer appears automatically in the LAN tab in the GE:S client.  I have to manually specify an IP or hostname to connect to the server.  If I remove +ip 192.168.0.100, I get the server back in the LAN tab, but no rcon access.  Flagging rcon_address seems to do nothing.
I have double-checked that all clients are on the same subnet, same VLAN, even the ports on the switch are all set to access.  I have no internal firewall or rules blocking traffic internally between clients.
Ideas?
No LAN Autodiscovery, have rcon access
#!/bin/sh
export MALLOC_CHECK_=0
cd /home/steam/steamcmd/srcds/
./srcds_run -game ../gesource \
  +ip 192.168.0.100 \
  -port 27015 \
  +maxplayers 16 \
  +map ge_archives \
  -debug > /dev/null &
LAN Autodiscovery, no rcon access
#!/bin/sh
export MALLOC_CHECK_=0
cd /home/steam/steamcmd/srcds/
./srcds_run -game ../gesource \
  -port 27015 \
  +maxplayers 16 \
  +map ge_archives \
  -debug > /dev/null &