Interesting take,
But your assumption is a little weak. Unlike most pirates, William Kidd was arrested and put on trial, so the details of his travels are fairly well documented. The stash that Kidd had tried to use as leverage to bargain for his life was valued at £100,000 pounds. This coincides with the estimated plunder taken from the QM. Henry Avery's hoard was reportedly worth over £600,000 pounds (The equivalent of £115 million today). If Kidd actually had access to Avery's treasure, then why didn't he mention it when his life was at stake?
Also, Avery had no reason to bury any of his treasure. After the "heist", Avery was so wealthy that he immediately "retired" from piracy and lived the rest of his life in very comfortable obscurity.