Aaron's tombstone has his age as 71 years. This puts his birth date as 1693. That makes a gap of 3 1/2 to 5 years from Aaron's birth to the Bevis Marks wedding for Jacob and Rachael. I have evidence that both of these families noted in the Bevis Marks records were "Marranos", so in all fairness to Jacob and Rachael they may have been married with Christian rites before Aaron's birth. This would all but eliminate London as Aaron's birthplace because at that time frame (1660-1698) London had a thriving Jewish Community.
I think Aaron was born in a different country before they came to London. This assumption would fill in the gap we have already noted and make it easier to accept 1698 as the year they arrived in London.
If we could find good records of Aaron's birth "several" questions of the early family history may be answered. If any one has documentation or can direct me to a source for Aaron's birth records I will be very grateful. Haven't had any luck so far. Thanks for the reply and if you are interested in the information about these families being "Marranos" e-mail me.