Wow, this really sounds like a trip I wouldn't want to do...
- One way SF-JFK
- Last minute reservation
- No Insurance
I would be sure to look at all companies; I would be surprised if Hertz was cheapest for this trip.
I would also be certain to NOT pick up the car at an airport; a HLE location or in the city will be cheaper.
I did a quick search on Orbitz to compare companies. I found Budget, picking up in downtown SF tomorrow, returning to JFK on the 31st, for $1500 all-in. This was for a full-size car, which the same price as a midsize and compact. Econonomy came out much more expensive for some reason. And when I tried to book this on Budget's website, it was also much more expensive.
There are lots of other options for long-term trips like this, but at this late date I'm not sure you'll do much better than $1500 quoted above.