Exactly the people who SHOULD be doing these experiments. If you want to know if soemthing was done fraudulently, why not go to people who know who to commit fraud? Scientists are generally pretty poor at recognizing fraud... look at the history of ESP experiments and the like.
Why do you think a professional magician would be any help? Most of the PURCHASE their bag of tricks from engineers who design them for them. ESP experiments were real time examples of misdirection and sleight of hand with living subjects demonstrating a supposed "talent.". Misdirection and sleight of hand has nothing to do with an existing artifact. Every attempt by one of these magicians to recreate the Shroud has resulted in a ludicrous failure.
In other words... "none."
No, there are the known cultural, historic, and specific burial practices of the 1st Century Judea and Jews. There is the fact the mouth is closed (supposedly after sever days and or hours), the curious question of the appearance of the hair and beard being thrust forward. These are all forms of evidence.
Is there a visible chin strap? No.
Does there have to be visible? No, based on observation and knowledge of history and culture, including the knowledge it was a common practice, makes it a reasonable inferance.
Are Jews the only ones to use a chin strap? No it actually was and is a fairly common burial practice. In the United States, the morticians SUTURE the mouth and eyes closed.
Is it possible that rigor mortis is keeping the mouth closed? Possible, but unlikely. The Man on the Shroud died in agony, probably with his mouth open to help him breathe or to scream. It certainly would have fallen open on death by the force of gravity alone. Rigor would have left him agape instead of closed mouthed.
And so on.
All the evidence points to some kind of binding keeping the jaw closed.