A FPID card is only required to purchase, correct. It is not needed to shoot or transport a gun to an FFL/gunsmith/range/ect, provided you don't make any unnecessary intermediate stops.
NRA-ILA
Lots of misconceptions about it (along with people who think you need to register your guns and that JHPs are strictly illegal) but most of the ranges seem to understand the operative word in Firearms Purchasers ID. Be aware, however, that if you don't have an FPID you can't even finger-bang a gat at your favored venue of arms sales.
Without an FPID you cannot buy pistol ammo in person in NJ. However, you can order online and have ammo shipped to your house (unless that changed recently, which I haven't heard). Some vendors won't do it unless you fax them a copy of your FPID. Ammotogo, Cabelas, and Sportsman's Guide do not, as it's something to do with the fact that NJ cannot regulate interstate commerce, only the sales of ammo inside their borders. Completely legal. My UPS guy got tired of hauling 50lbs of ammo to the porch, however.
You may also want to consider shooting in PA. There's a few ranges in Philly, as well as Ready, Aim, Fire in Bristol (rsa-otc used to be a member) and Classic Pistol in Southampton (I used to be a member).