Lot of empty stadiums there. And why would any school sign up for this? You have 4 schools selling tickets for a double header, so each school only gets 25% of the gate receipts. So using the Rutgers game you propose at MetLife Stadium, we get to sell about 20,000 tickets to this double-header, and we get to tell half our season ticket-holders and students to take a hike, or we can have the game in Piscataway, and sell 50,000 tickets (including students).
I kinda like the idea of making the Lambert Trophy more of a thing. Besides, East Coast football could use a shot in the arm from a national advertising standpoint.
Neutral site games could absolutely work and draw interest. Call it the Lambert Trophy Eastern College Football Series presented by AT&T or whatever. These can't be doubleheaders. From a tv perspective, ESPN should be able to get (and brand) these games, except WVU home games and Army-Navy, of course.
For this to work, you can really only rotate between the P5 Lambert programs: Boston College, Penn State, Pittsburgh, Rutgers, Maryland, West Virginia, Virginia, and Virginia Tech. The Army-Navy should be a "protected" Lambert game. Clearly, the Lambert brand would take a backseat to the Army-Navy brand, but Lambert should be part of it.
Year 1 could look like what's below. You'd have to get the ACC, Big Ten, WVU, and Army/Navy to agree, create a rotating schedule, and secure contracts with the stadiums. Not easy, but not impossible.
Metlife Stadium
BC vs. Rutgers
Lincoln Financial Field
Pittsburgh vs. Penn State
M&T Bank Stadium
West Virginia vs. Maryland
FedEx Field
Virginia vs. Virginia Tech
Rotation of MetLife/M&T/Lincoln Financial
Army vs. Navy
The Big Ten wants to get away from off-campus anyone, so I think that makes it a moot point.
I think it'd be fun even if the games are played on campus.