S. sent me the very interesting collection of letters of Shadal's cousin Shmuel Chaim Lolli. Some of the letters discuss Shadal's Vikuach Al Kabbalah. In the discussion of the prophetic power of dreams on pg. 82 (recently referenced by Eliezer Brodt in his magnificent post here), Lolli records the following anecdote:
I think its fascinating that A - this "miracle" is very similar to the many wondrous stories that circulate today. B - The phenomenon of women reciting Perek Shira is not a product of our own era.
I thought it odd that this "prophecy" was delivered to the gentile maid and not to Bas Sheva directly. If a rational explanation of this story is needed, it is not impossible that the gentile maid would have heard Bas Sheva lecturing on the benefits of Perek Shira at one time or another which later surfaced in this dream.