I did that commute for about a year and had no trouble at all. Although I'm not sure where Brown parks at EWR, FedEx guys can park in the employee parking lot. The lot is served by both regular crew buses, which can take you over to the passenger terminal, and FedEx buses which take you to building 347, which is where you'd go through security screening and then be escorted upstairs to FedEx flight ops.
As for the cost of parking, when I changed domiciles to ANC, I called the lady at FedEx EWR operations and asked her for an electronic parking pass. She made a big thing of it, and told me that the cost would be about $60/month. I said fine, and the next time I got to EWR, the parking passkey was ready. I used the passkey for the year I did the commute, and never once received a bill or a payroll deduction for parking. We even got a note that said the price was going up, but again, they never charged us.
Jumpseats were always available, and the MD-11's left almost every night at about 2 A.M., arriving Anchorage at about 7 A.M. Sometimes they had the captain-in-the-box configuration, and on these, you'd have to get the Captain's permission to ride. I was never turned down, and the beauty of it was if I was the only jumper, I got to use the bed. Flights left ANC at about 2 P.M., arriving back in EWR at about 1:30 A.M. Again, flights were usually available for jumpseating.
Hope this helps. The times might be a little off, but in general, that's how FedEx operates.
Good Luck.
JJ