https://www.bonhams.com/auctions/20495/lot/180/
This is an interesting collection circa 1903/04. The 19H single scroll elephant badge is flanked by elephant collars which matches your dress regs. These are brass OR badges and of a similar design to the larger 1920 pagri badge. They also appear identical to the Connaughts' collars.
The OR's cap badge in the Bonham's collection is the 'wrong' scroll title for the 1904 dress regs; which do suggest that the double scroll badge with 'Alexandra' in the title was the official officers' badge at the time. I can't say that I have ever heard of a Bronze double scroll badge though.