It was actually easy to configure XP to look up local names from the DNS server on my router. I did not need to bother with editing text files.
There is a place in the DD-WRT GUI where the LAN domain is set for DHCP. In the screenshot below, you can see under Administration-> Services, there is an entry for LAN Domain. Set it to a domain name of your choice. I chose localnet. Be sure to save your changes. I did not find it necessary to reboot the router.

On the XP side. Go to Control Panel-> Network Connections. Right click on the correct adapter and select properties. Then select Internet Protocol (TCP/IP) and click Properties. On the General Tab there is an Advanced Button. This will bring you to a dialog where you can choose DNS Tab. Click on the radio button “Append these DNS suffixes (in order)” Then click the Add.. button. Add localnet to list. No rebooting necessary.

I’m sure there is an easier way to navigate to this buried dialog box, but that’s the way I navigated there.
Posted by benjamenjohnson as computer, linux, network at 4:57 PM UTC