No 1 project is a magic bullet here. Gateways full potential won't be realized unless capacity is added in Penn, capacity expansion in Penn won't be realized unless Gateway is done. Likewise for any projects for LIRRs benefit. Me personally I'd suggest Tracks 1-5 and Penn South get under the East River connecting to both the main line and the lower Montauk. That way, NJT & Amtrak trains coming into those tracks can access Sunnyside rather than terminating at Penn, and LIRR could get added capacity (let LIRR take over E yard). Hooking into the Lower Montauk also allows trains an alternate route to the main line, which also helps with sorting at Jamaica by eliminating merges. That's really the only way you'll see the most made out of Gateway & Penn South.
Also, are they saying the need to demo the block Penn South would be under because building foundations are in the way or is it for a headhouse? If it's for the sake of a head house, they can do plenty without demolishing the entire block. There's a parking garage that could demolished to provide sufficient access (either leave it open as a pedestrian plaza or redevelop the space above it) as well as 2 low level commercial buildings closer to 8th Av whose storefronts could provide secondary access.