I now have this working. Here are the steps I took.
1. Install TinyDNS (System -> Packages -> Available Packages -> Install dns-server)
2. Added new domain to Tiny DNS (Services -> DNS Server -> New domain wizard)
During this step, I added my domain (foo.com) with a number of initial hosts
3. Configure Tiny DNS (Services -> DNS Server -> Settings)
I set the following:
Enable recursive DNS responder: Disabled
IP Address: 127.0.0.1
Interface to listen: loopback
I left all other settings as default
4. Configured DNS Forwarder (Services -> DNS Forwarder)
Enable DNS forwarder: selected
Interfaces: LAN
5. Added domain to overwride (Services -> DNS Forwarder -> add Domain Override near bottom of page)
Settings here are
Domain: foo.com
IP address: 127.0.0.1
6. Ensure that your ISP's DNS servers (or whichever servers you want to forward to) are configured under System -> General Setup
This is now working. All requests for my domain are handled by TinyDNS and everything outside my domain is handled by the forwarder.