Give it a try
NFH is currently working with Congress to introduce legislation that would have the Forest Service issue permits to rebuild on lots such as the one you describe. NFH is gravely concerned about the significantly declining number of cabins and want to have cabins rebuilt on lots already authorized for use as recreation residences. The advocacy effort is described here on our website. The page also includes a link to submit questions or comments if you want more details about how your situation over laps with our national effort.
My advice to you is to approach your District Ranger as there are some supportive agency line officers. Knowing the response (any answer: yes, no, maybe) would be useful to our national effort as well as which National Forest you are in.
Regards,
Meredith Randall, NFH President