If you are out-of-state and need a replacement Florida drivers license, you can only receive a 90-day temporary permit. There is no fee for this permit. To request one, you can call(NNN) NNN-NNNNor mail a request to Bureau of Records, 2900 Apalachee Parkway, MS 92, Tallahassee, FloridaNNN-NN-NNNN You must include your full name, date of birth, social security number, Florida driver license number and an out-of-state address. To receive a new drivers license you must be present at a driver license office in the state of Florida."
As you can see, you can obtain the temporary duplicate license, but is only good for 90 days; then, to get your new license replacement, you will need to do it in person at a DMV office in Florida.
To replace your registration:
"A vehicle registration may be duplicated at any county Tax Collector Office or License Plate Agency for the fee of $5.00 or from the departments website"
It appears that you can only do this in person, but if you get in contact with the DMV in Tallahassee at the above number, I'm sure you can find out more, considering your extenuating circumstances, being in New Jersey at this time.
I wish you much good luck and hope you are able to get a duplicate license and registration without too much trouble!