The airport bus recommended above from Jackson Heights/Roosevelt is quick and cheap. I think it will be next to impossible for the new train setup to compete on any level. TBH the main benefit of the airtrain is that it will keep people from LI, and parts of Queens and Brooklyn from driving to the airport (which is what they do now). Even with more LIRR trains (highly unlikely as noted) this will be longer and more expensive. And of course the timing to Penn Stn does not account for getting from there to your destination. Give it a try or another one.