Is it sufficient to audibly praise God for the first sneeze, and then do so silently for the remainder, to avoid burdening neighboring worshippers when sneezing repeatedly in the mosque?

It is prescribed to praise Allah every time you sneeze, even if you sneeze frequently. Do not let the fear of disturbing others prevent you from doing so. You may praise Allah silently, for praising Allah upon sneezing is a recommended act, not an obligatory one, and it is not required to say it aloud. Furthermore, it is not necessary to say "Yarhamukallah" (May Allah have mercy on you) to the sneezer more than three times.