Take your box with well packaged weapon and some of your other gear shoved in for good measure to a UPS Customer Center, not an outlet or a store but a Customer Center. You can find them online by going to UPS's webpage for a location near you.
Ship it by UPS Ground. From West Coast to East Coast, the travel time is four or five business days.
Ship it to a different UPS Customer Center near where you are going or somewhere on the route you will be taking when you're back east. Gettysburg has a UPS customer center in case you're wondering. Been there. Been to the one in Buckeysville, MD, too. You're actually going to ship it to yourself care of the UPS customer center of your choice. They refer to it as a "hold for pick-up." Some UPS customer centers have limited pick-up hours so you should look at their schedule before sending.
They will hold it for five business days. Bring your ID because they won't release it to you without it. By shipping it to yourself, you don't have to worry about UPS leaving it at someone's front door and someone else walking away with it.
I like my stuff to arrive by the Tuesday before a weekend reenactment. To the East Coast, I generally ship on the Tuesday a week before a reenactment because it's a five business day trip from the West Coast. This gives them a couple extra days to get it where it needs to be.
I've been shipping my gear and weapons this way for more than ten years. In declaring your weapon in your packing description, please note that it's an "antique muzzle loading musket." UPS and other agencies get weird about modern, cartridge based, breach loading rifles because the rules are different for antique verses modern weapons. I ship my rounds and caps with my weapon but always double or triple wrap them in plastic bags.
Don't write GUN, GUN, GUN all over the box. UPS will attach plenty of fragile stickers on it for you if you ask - which you should.
When you go home, ship it back to yourself the same way you got it there. I always make a double thick box and go through lots of clear packing tape to make sure the box is strong and can be reused. (Just tape over the dents incurred from the original shipping trip.) Don't forget to include packing tape with your luggage. That way you'll have it when you need it later.
Cost each was is thirty five to fifty dollars depending on how much other stuff you throw into the box. You should ship your blanket, shelter half and gum blanket with your musket as they make swell packaging when you wrap them around the weapon.
"While the original battle [Gettysburg] may arguably be considered the epicenter of the history of the war, the GAC reenactment is not the epicenter of the hobby. To confuse or equate the two is unfortunate. - Bernard Biederman, 6 July 2012
"Authenticity conflicts occur when reenactors from one end of the spectrum attend events at the other end of the spectrum then try to impose their own standards instead of event standards."