Right to reimbursement of transportation from JFK to EWR or a nearby destination is absolutely applicable, as per Article 8, paragraph 3. of the Regulation (EC261/2004).

Ask at check-in whether they can give you a voucher, or if you should ask for one at JFK. If you don't get one, take the Uber and submit for reimbursement.
They will reimburse you, although it might take some time.

Asking for anything else, well too late for that now. You could have asked for rerouting at better times, but now your flight is whatever it is.