Building 7 to Secaucus and building a station in the Sunnyside area (or revamping Hunters Point Avenue station, that has terminating platforms for LIRR trains may be a more effective and less expensive ways of reducing pressure of Penn Station. The side benefit is dispersal of point of arrival into the Metropolitan Region thus reducing pressure on Subways around Penn Station, something that is also possibly achieved by running through, but less so than improving connectivity into the Core from peripheral stations using Subways
This could also make it easier then to run through just a subset of trains without costing another arm and leg for building more new infrastructure. But of course, new multi-system rolling stock will still be needed as the currently available rolling stock won;t make it across the Hudson Ocean from the NY side
There are many ways to skin a cat. But most of the proposal that involve cooperation between MTA and NJT will most probably not happen without restructuring the organizations and changing their primary goals significantly.
In any case I would be very surprised if even an agreement on doing any run through happens before 2050, let alone implementation, and finding the funding for it.