John,
There is a lot of interest and people out hunting space rocks everyday. If the USFS that you are looking into allows detecting then Space Rocks are on the table. But do you know where to hunt? In NM the Glorieta strewn field is one of the most popular and very well known for some great meteorites.
There are a number of books, maps and chatter about Strewn Fields on line.

If your detector works well for iron and good for getting gold, you have a great detector for meteorites. Just remember that you’re going to have to look with the iron discrimination turned off.

Kevin provided good information about strewn fields, those are definitely the best places to look for meteorites. Also, you can also get more information on meteorites and strewn fields with maps by state here: https://www.lpi.usra.edu/meteor/

You mentioned something about a claim? Although Meteorites are not claimable materials on mining claims, just be sure the owner clearly knows your intentions and do not to disturb the ground on a mining claim. Personally, I wouldn’t use a detector for anything on a mining claim unless given permission by the owner.