I forgot about it for a while but then came across the part in The Power Broker detailing the many failures of city works under Tammany in the 1920's and there it was. The Narrows Tube,
The Google turned up some interesting history:
The trans-narrows tube would have shot people and cargo across the Narrows
from St. George to Bay Ridge. The proposed two-mile tunnel section, which alone
would cost about $27 million, would have been the longest underwater tunnel in
the world when completed in 1929. But years passed and the tunnel project sat on
the city planners' shelves neglected. Work would halt a year later and petitioning would begin again. The incomplete construction of 1923 would turn out to be the closest Islanders have ever come to getting a rail connection to the rest of the city. (From the Staten Island Advance)
The NYC Roads page for the Verrazano Bridge has a history of the bridge that includes a history of the still-born tunnel from Brooklyn to Staten Island.
Saving the best for last, the NYC Subways page for the 4th Avenue line
details how the R train would have been extended out to Staten Island:
The original Dual Contracts plan provided for a tunnel under the Narrows from southern Brooklyn/Bay Ridge to Staten Island. The tunnel was intended to
leave the 4th Avenue subway at 65th St, Brooklyn, and would have entered
Staten Island midway between St. George and Stapleton, and would have had
branches to each. The 4th Avenue subway has four tracks between 59th and
65th Streets, two of which were intended for the Staten Island connection.
The Staten Island link might have been built in several different ways.
It is likely that a full 4-track subway to Fort Hamilton would only have
made sense if it led to a Narrows tunnel. A different plan, which got as far
as engineering drawings and even some excavation, would have left the subway
just south of 59th St, and you can see tunnel stub headings running straight
from the local tracks immediately south of the station. Several different
plans were drawn up for the Narrows tunnel, including a two track and a four
Recent discussions of a railroad freight tunnel across New York Harbor from New Jersey via Staten Island may once again bring about discussion of connecting the subway to Staten Island. It is likely that any tunnel built would be designed to tie into the LIRR's Bay Ridge Branch across southern Brooklyn to East New York, Fresh Pond, and via the New York Connecting Railroad to the Hell Gate Bridge.
Put this down on my wish list for transit projects. If anyone knows about traces of these tunnels that can still be seen/explored, please let me know.