Well first to put a needed footnote to one of
your technical-regulatory positions.  True FRA
regs prohibit running light and heavy rail on
the same track.  However, exceptions exist and
the most important exception is over in Jersey
where Hudson-Bergen runs part of its way on heavy
rail track.

Second, you posit many neat systems, most of
which would still be running if this were Europe.
But,until you posit a way to pay for it you have
really stated nothing.  Staten Islanders have
a thousand reasons why the Ferry should run for
free, why they should have a discount on the
Verrazano, why the Staten Island Railroad should
have the lowest fare-box recovery of any MTA
system.  Never will you find a Staten Islander
who will agree to pay a toll increase for
anything.  Yes there are many interesting systems
as long as someone else pays for them.
 

"However, exceptions exist and the most important exception is over in Jersey where Hudson-Bergen runs part of its way on heavy rail track."
False. The HBLR doesn't even have any track connections to the mainline network. However, the Newark City Subway and the South Jersey Light rail both have some shared track. However, there is a strict time separation there, with freight trains having the line at night, and light rail at other times. That's why light rail service ends relatively eary on both of those segments.
Just for the record, the ferry is free because of the MTA's one city / one fare system which allowed free transfers between bus and subway for the first time (I believe this only started in 1997) with the formal Metrocard launch. Before then, Staten Islanders commuting to Manhattan faced a three legged commute - bus/train to ferry to bus/train. And the ferry is not that expensive to run and operate and takes many cars off the road.

Remember that all other boroughs have free bridges to Manhattan: Brooklyn Bridge, Queensboro bridge and many free bridges between the Bronx and Northern Manhattan.

Just like anything else, these types of large infrastructure projects are financed through a mixture of federal, state and local money combined with the farebox.