ElBow513,
There are many smaller cargo carriers that fly all over the US. Some fly the mail. Some fly UPS or FedEx stuff. Some fly canceled checks. Some are there for on demand charter. There are literally hundreds of these outfits all over. I'm sure there are more of them than I can name, but some I can think of are Mountain Air Cargo, Empire Aviation, Airnet, Paragon, Cherry Air, Kalitta, Ameriflight, Air Cargo Carriers, Wiggins Air, USA Jet, and Ameristar.
Some of these are nationwide, some are local outfits. Some may fly better equipment than others. Some may not even be around anymore, these are just the ones I can think of.
Some of these have jets, some have piston twins, some have caravans. Try to get in a turbine twin if possible. This is what you will need to get on at any major, including FedEx.
Look around the web and see what you can find out about these folks. flightinfo.com has some info as well.
Good luck.