After speaking with the Navajo Nation/San Juan River office in Window Rock, they seemed OK with sending in application for backcountry permit without putting down the exact date or location. I received an email with scanned copies of my permits in about a week after mailing in the application. I just wanted to have the option and flexibility of using one night at my discretion and they seemed OK with that.
Can't say it will work for you, but it worked for me
I thanked them and mentioned that they may want to consider revising their permit for river runners to make it easier (I gave the example of the Ute permit for Deso).