Darn! I thought the site was closed to the public long before when this forum post was listed. I would have made several trips. The NJ amber is some of the oldest in the world. If the site is really gone, this is a tragedy for science. At least there are still a few great river sites in NJ available for shark teeth and other fossils. Wish I had the chance to dig some amber while it lasted.
I've cut and polished amber with my regular lapidary unit. Amber is so soft that the grinding wheel is not really necessary. The material can be completely shaped and sanded on SC sanding belts, wet. I polished with tin oxide (again, somewhat wet) and achieved very good results.
Unless you intend to go into lapidary seriously, I would just do the job by hand with wet or dry sandpaper (used wet.) Rough-in the shape with 100 or 220 (or a file), sand with 220, 400, then 600. Quite worn 600 makes for a good pre-polish. Actually, amber is so soft, you could probably go directly from rough shaping to sharp 600 for final shaping. Then worn 600 (or finer if you have it) for pre-polish. All sanding steps should be done wet - no heat, as has been noted. I polished with tin oxide on a felt wheel. The same thing could be accomplished by hand.
Having said all that, a dealer in the Dominican Republic (where most of the world's fine amber comes from now) told me that most amber there is polished with gasoline. I haven't tried it.