I wrote to Hajj Information website, and the reply is as follow. Hmmm, previously I thought that Ministry of Hajj have all the information
Thank you for your email. You explain your plans very clearly.
We suggest you consult your Umrah provider to determine whether departure from a different location from the point of entry may cause problems.
Alternatively, you might ask the Saudi Embassy/consulate in your country for advice.
We do provide some information on visas but we do not have enough information to answer your questions with certainty.
Haj Information webmaster