Tom,
I like the idea however there have been studies made on why buttered bread seems to always land butter side down when you drop it. Its puzzled people for centuries.
That may not seem like a fair comparison to your tennis shoe however it has been a historically asked question that bothered someone to investigate it... and no, no real answer has been found but there are a lot of good sounding ideas on the subject.... much like dowsing

Take this as a simile for the following arguments to your suggestion.
I don't take your suggestion as nuts. The question is would I do it? Sure. Only if you provide some sort of intelligent reasoning or you can provide some sort of hypothetical and/or historically based evidence that somehow the tennis shoe combined with peanut butter and birdseed would point me to treasure after having been thrown in the air. After that I'd probably want to see your suggestion in action: Preferably by you

As I said I strongly support scientific method; however I do keep an open mind to strange unexplained things as the following thoughts suggest. The buttered bread argument
Now remote viewing : No ones ever given me a practical explanation and nor have I ever seen it practiced however the studies have been done and there is historical evidence backing the claims. The results from what evidence I have perused suggest there maybe something to it and its strange. So, yes, I do keep a weather eye on such claims. Does the bread fall butter side up or down?
Now dowsing: I've both seen and demonstrated this technique for locating items. There have been studies on it and it has historical evidence backing it up.
As such I do believe such methods of locating items may work. However this method does not lend itself to repeatability in a controlled environment so I must chalk this one up to being strange too. But its believable. Our best minds just have to crack the reasoning to the observed phenomena yet. Butter side up.
Now a tennis shoe smeared in peanut butter, sprinkled with birdseed and tossed in the air to land pointing in the direction of the seekers desire after which one would strap on a metal detector and go find.... lets say gold bricks buried by a super secrete government project on remote viewing studies.
No studies or demonstrations of such activities have ever been presented to me nor have I ever seen or been presented with historical evidence that such a technique exists. I see no practical reasoning why it should work but it is a fun suggestion. Why? Hehh hehhh..... butter side down. HOWEVER, I shall attempt to put the butter side up in your suggestion....
1: In the phenomena of dowsing there is a method that uses a pendulum to locate items of the seekers desire. Now the pendulum is often made of the material that the seeker is looking for and the pendulum is held by its string over a map, or carried in the field. The seeker uses the reaction of the pendulum to narrow down their search area for that which is desired and then digs for it.
2: I would not throw the tennis shoe covered in peanut butter and sprinkled with birdseed in the air. I would instead take said shoe and hold it by its shoe strings and use it like a pendulum. Hover it over a map and go see what I will see where the pendulum has its strongest reaction. Now considering the materials of said shoe this is what I expect to find
A Jogger who's a health nut and had peanut butter for breakfast and a birdseed granola bar.....

......
Or someone in the park with a peanut butter sandwich feeding the pigeons while wearing tennis shoes....
Now as to strapping on a detector and going in the direction of said fallen shoe.... btw you did not indicate whether your following the toe or the heal and I don't necessarily assume the direction.... Yes you will probably find something and hence your treasure
