You know anybody in Brooklyn you can stay with ?
It's a sound idea, but as you discovered, details, details.
Maybe later LIRR and then NJ Path to somewhere convenient south of Newark ?
FWIW, the SW Nassau to middle of Brooklyn is my 25 mile one way commute. I think the distance to lower Manhatten is about 35-40 (via Coney Island and around the south end of Brooklyn via the shore path),
so at least 2-1/2 hrs, which makes for a really early start, depending on where on LI you start.
SB