According to what you wrote, el service
went to Rockaway Park, but only for a few months.
That's what I thought he wrote too, but I believe it was the LIRR
steam service to Bway Ferry that lasted only a few months.
The BRT operated steam on the LIRR connection until the Chestnut
ramp itself was electrified in 1906. At that time, LIRR MP-41s
began operation via Broadway to the ferry, and later to Chambers
St. once the Centre St. line was finished.
BRT electric trains ran to Rockaway Park until 1917.
The LIRR used covered third rail, while the BRT els used exposed third
rail with gravity shoes. It seems that the LIRR MP-41s had
a universal shoe with two height settings. The BU cars which were
used for this service must have been fitted with paddle type shoes rather than gravity because all pictures I have seen of the Rockaways during the joint service years show covered third rail.