Call the SNF office in Prather and explain what you are doing. You want to hike from Mono Creek to Whitney (exit), and are hiking from Mono Pass to get to VVR.? (This is a true statement!) They may have a solution for you.? They have been very helpful to me in the past, although not like this. They don't have a lecture to give you for your permit, like many jurisdictions. For example if you are passing through Prather before or after office hours, or days before your permit date, they will leave it in a drop box on the office porch. There used to be a permit office on Kaiser Pass, much closer to VVR than Prather, but it hasn't been open since COVID.? The point is, they are helpful.? Perhaps they will mail it to you.? Perhaps they will have a ranger drop the permit off for you at VVR.? It's worth asking.
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Also, be aware that the trail from Mono Pass to the JMT junction may be in rough shape. I haven't done it, but want to some day. I have seen reports in recent years that there are lots of blow downs, and SNF is underfunded and I haven't heard of any trail maintenance done there lately.
