I visited Nagaland 2 months back. Faced the same problem. But apparently ILP is not required. We just paid an entry fee of rupees 100 on reaching dzouku valley.
Anyone can apply for a provisionalILP(valid for 30 days ,same as tourist ILP) with limited number of documents(only one of PAN card or Aadhar card or Voters id). When applying both online and offline, you will get a verification SMS on submission .Depending on workload your application will take hours to weeks.
If there is any Nagaland house where you stay You can go and take it out from there. In case if its not there then to visit Nagaland you anyway have to come to northeast and have to go through the gateway to northeast; Guwahati. So, what you can do is visit Nagaland House in Guwahati, located in Sixmile, Sachal. You'll need any Govt. ID. 2 passport size photograph, And 100 rs per person charge for the ILP. Ph. No. 0361-2332158. When you are in Guwahati you can locate Nagaland house in Google Map. A very easy destination to find out. You have to be on the GS (Guwahati-Shillong) road. I hope that helps.