Updating on this thread, which I found high up by Googling:
Amtrak baggage check (which is also a temporary storage) is still at the same place, works 5:15am-9:45pm, cost is $5.50 per item.
NJTransit ticket WORKS FINE; LIRR does not - I asked the agent about both.
I bought a NJTransit ticket to Secaucus ($4 one way, says valid until use; there's no date on the ticket. Figured I'll use it one day when going somewhere in NJ or to EWR) and it worked without a hitch. Beats going to 36th street and paying $7-10 per item.