https://www.google.com/books/edition/The_Visitations_of_the_County_of_Surrey/naxCAAAAYAAJ?hl=en&gbpv=1&pg=PA42
Stydolf is here on page 42
I had already entered the baptisms for several children at Mickleham
So I can report that the Henry/Harry by the third wife was bap 20 May 1572 Mickleham, Surrey (Batch C14520-1 wj)
There was also then a Suzanne in 1573 and an Elizabeth in 1574
Since William, son of William, here, is called "aged 33" in 1623, then the Henry I mentioned cannot be the second son who was by Jane Gyles, but rather he must be the fourth son, by this third wife Jane Smyth
This gives an approximate date range for this third wife, whom I had not otherwise known about.