I just went through the reset process a bunch of times with no luck. I was able to get it to work when I set a static route for the wired connection for the network 192.168.1.0/24 with a gateway of 192.168.1.2. This is after manually setting the IP on the wired connection which is the LAN Turtle to 192.168.1.2.
I was then able to restore the firmware on the LAN Turtle.