You might like to believe thats an insurmountable problem but the PRR modified the 1.5 mile baltimore and potomac underwater tunnel several times. The first time the floor was dropped by 2 and a half feet in 1917. Park avenue doesn't have millions of gallons of water of it so why not enjoy lower operating costs, and higher speeds.
On the LIRR, full cantenary isn't necessary as the majority of its branches don't have the distance to justify it. However replacing it on the Ronkonkoma and Port Jefferson/Huntington lines would create numerous benefits..
1. Ronkonkoma runs at about NEC regional station spacing from hicksville to Penn and perennially comes up as an integral part of an alternative HSR path to Boston from the penn design group. Adopting NEC regional speeds would do much to extend the viable commute distance for the good people of eastern long island.
2. Those running costs aren't fun. Port Jefferson to Huntington costs 100 million to operate with an abysmal 23% farebox recovery, while Huntington on and Ronkonkoma are carrying about 4 times the passengers each for ~150 million a piece.
3.It would also be the best way of enabling through running at penn. Ronkonkoma could go to new jersey transit's NEC portion. Trying to do it haphazardly with dual modes will never be able to realistically add capacity with their high running costs.
As for funding John Mica won't always be around to focus the House Transportation committee on grinding his axe against Amtrak with constant hearings on dismantling amtrak. Amtrak's master plan for the NEC projects its real funding coming in when those has-bens Mica and Shuster go into the night. Transportation infrastructure spending is the best performing job creator with its stringent Buy American clauses. Once we pass into more enlightened times where the focus has shifted away from zeroing mass transit funding in the name of defeating the imagined socialist threat, Hopefully when those times come spending will be focused on increasing efficiency than building some senator's vanity project to build HSR in the boonies.