None of the run through plans will remove the bottleneck at A Intelocking inside Penn Station and at Harold by Sunnyside. Indeed it could make the situation worse at Harold potentially putting more trains through it. A interlocking congestion mitigation will require the building of at least one tunnel under 31st street providing egress from tracks 1-4 to Sunnyside.
I seem to recall that there was a proposal for connecting 5 platform tracks at Penn Station to the lower existing level of Grand Central Terminal. Were Penn Station's tracks 1-5 the ones that could be connected to GCT in that fashion?
I'm wondering if a viable operating plan for a NYP-GCT connection might be to have NJT run about a dozen trains an hour in NJT's peak direction through Penn Station without stopping at Penn Station, with their only Manhattan stop being GCT, and then have them continue along Metro North's Park Ave track as what Metro North would view as reverse peak trains, possibly just deadheading to the nearest yard. One challenge with this is it is not clear to me that there is a nearby yard readily reachable by the existing tracks.
In addition to that, Amtrak might run various trains through GCT to whatever extent Amtrak could work out the power issues.
On the one hand, Metro North may not have any obligation to provide Amtrak with five slots an hour in each direction (if we're rounding up counting one Acela round trip, one Northeast Regional roundtrip, one Empire roundtrip that might run through to WAS, and a Keystone and a long distance train), plus a dozen reverse peak slots an hour for commuter trains from New Jersey. On the other hand, it appears that Metro North may have some interest in finding some way for some of their trains to reach Penn Station, and perhaps Amtrak should insist that they agree to share some GCT capacity if they're going to start using some Penn Station capacity.
There is the question also of what would happen with the loop at GCT, but I suspect that the Penn Station tracks could have a level crossing with the loop; if there were only five mid-day trains in each direction on the Penn Station tracks and 25 slots an hour, it ought to be possible to run 15 trains an hour through the loop during the mid day even if the Amtrak trains in opposite directions were never scheduled to coincide with each other, and if someone told Metro North that they had to figure out how to live with that limitation as a condition for getting into Penn Station, they might manage to figure out how to operate with that restriction.
I think this plan might work with one platform track at GCT for northbound Amtrak trains, a second for southbound Amtrak trains, and two platform tracks for NJT; that should give each train an average of at least 10 minutes with each platform track. Again, perhaps Metro North could be persuaded to figure out how to make these GCT tracks available if they are interested in using some platform space at Penn Station.
The reason I suggest having the NJT GCT trains not stop at Penn Station is that otherwise, they may very well run fairly empty from Penn Station to Grand Central Terminal after bringing a large number of passengers to Penn Station, and if only a limited number of NJT trains reach GCT, it is desirable to have them carrying passengers who actually wanted to go to Grand Central Terminal. Perhaps Secaucus Junction would be a useful transfer point.