Just electrify all the remaining track with high voltage AC catenary. It'll be roughly 1/2 the cost of electrifying with 3rd rail, provide greater transmission efficiencies with lower voltage drops, and it'll allow locomotive hauled trains to run at greater speeds than the 3rd rail would support. Start stringing wires at Mineola, Huntington, Babylon, Hicksville and Ronkonkoma and work your way east. It'll cost less to do the entire system now than it'll cost 25-50 years down the line when those lines are exploding and the DM30s are ready to croak. You folks are just lucky that the Pennsylvania railroad took a somewhat long term look at the LIRR's operations and Europe has proved convincingly that the one-time technical barriers that kept locomotives consigned either to AC or DC inputs are now obsolete, and a locomotive which runs off both the NEC's 11.5kvAC catenary and LIRR's 750vdc 3rd rail is not only completely doable, it currently exists in the form of the Siemens Eurosprinter ES64F4. This locomotive forms the basis of Germany's Class 189 quadrisystem freight locomotive and it's Swiss derivative the Re474, as well as Austria and Slovenia's trisystem locomotives. The electronics of the ES64F4 is entirely modular, and due to modern power electronics it is capable of readily having it's DC input bus adapted to handle voltages as low as 600vdc and currents as high as 1500-2000amps from the current 1500vdc and 1000 amps. I have dubbed such a tri-system locomotive the 'ALP48' since it could concievably bear a striking resemblance to the highly successful import locomotives which NJT recently recieved, although an MN model running on the New Haven line would do better to be called the EP-6. Bombardier, the maker of the NJT ALP46 could just as easily create a locomotive of similar capabilities as the Siemens ES64F4 out of their Traxx line of modular locomotive, and it's possible Alstom could do the same thing with their Prima line of locos (even though they've had problems lately), so by no means would this end up a single supplier contract or something otherwise troubling.
With such a locomotive, capable of 8000hp on the catenary and at least 4000hp on the 3rd rail, LIRR would be able to electrify the distant diesel branches, ridding themselves of the troublesome DMs (which would likely do well stripped of their 3rd rail equipment and sold to someone like Nashville, TRE, Metrolink, or VRE), begin a transition to a more universal and more efficient electric transmission medium, and yet not need to buy new MUs to cover the newly electrified sections immediately. The C3s are extremely well built and useful commuter coaches, and to replace them with MUs so early in their life would be a mistake, and best of all they could just as easily be pushed or pulled by tri-voltage locomotives as by the DM30ACs. Indeed because the locomotives could run on the Amtrak catenary from Harold to NYP only one locomotive would be neccesary on runs into the city, potentially allowing less than 30 electrics to do the work of 46 DM and DE30ACs. If the catenary were extended over LIRR to Jamaica then superior performance could be had on rush hour express trains around Jamaica in addition to eliminating the danger of the locomotives gapping out on the 3rd rail and the possibility for NJT and Amtrak trains to terminate at Jamaica if turning facilities were provided.
Sure it will cost money now, but it will cost less money than extending the 3rd rail incrementally for the next 50 years. If you think for a moment that LIRR funds it's own capital expenditures then you're sadly mistaken. Get the FTA to give a portion of the money for conversion of the diesel lines to electric and you'll have it set. LIRR may be broke when it comes to their operating budget, but the M7s and the ongoing construction on the ESA project shows that their capital budget still has funding. It would be in LIRR's interest to eliminate the diesel fleet, since once ESA is finished and peak hour slots open up at NYP they'll no doubt be called upon to supply more peak hour trains onto the Port Jeff, Greenport. Montauk and OB lines than the DM30ACs can handle. With only 11 sets of DMs, and allowing for 1 to 2 to be down at any time for inspections and maitenance, that's a mere 4 per line, which likely will not be enough to handle the crowds that will flock to the line once the areas out by Riverhead begin booming. 3rd railing would be nice because it maintains simplicity, but funding it would be difficult, especially when cheaper alternatives exist.