I do not understand how the dryer controller can assign itself an IP address.  The router issues the IP address, or makes record in its IP table of any static devices it sees on the network.  I really want to make this work for you but need you to provide the information I've asked for.  What make/model of router are you using?  Screenshots of port forwarding tables?  Screenshots of IP tables/leases.  Any other devices on the network?  Screenshots of IP config on the Watchdog.