Why not just set the empeg to a fixed IP address that matches your Ipaq's range? You can use the @AC and @DC modifiers with Hijack in the empeg's config.ini so that it keeps working in DHCP mode for when you bring it back into the house. Or heck, just set it and the ipaq to a fixed IP all the time, one that matches your house range.

If your wireless router is so slow at handing out DHCP address, you could (a) investigate and solve the problem with the router cuz it shouldn't do that and something's clearly wrong with it, (b) buy a new router that doesn't have that problem, or (c) just use fixed addressing on the computers on your LAN, since you've only got four of them.