Yeah, they are a reverse-mount wheel, which means the "bead seat" is on the inside of the wheel. The tire shops use the same equipment - just "backwards", if you will. They should have some plastic/rubber sleeves that slide over the clamps on their tire changing machine, so it does not damage the front face/lip of your wheel when they clamp it. They should break the bead all the way around on the front face of the wheel and only in one spot on the back. They will then clamp the tire/wheel face down onto the machine and use a (hopefully) protected duckhead and spoon to get the tire up over the bead-seat/lip of the backside of the wheel. It's super easy if they know what they are doing.
Also, I would definitely use the sticky weights. You can "static" balance them, but this will not be as accurate as dynamic balancing - only because they will use the sticky weights only on one side on the inner lip of the wheel, as opposed to inner and outer. You could try the balancing beads too, that you put into your tire, but I have no personal experience with those.
Current Whip: 2013 Mustang GT Premium
BAMA Tuned, Boss IM,Pypes cat-back exhaust, Lethal o/r x-pipe, Airaid CAI, BMR lca's w/ relo brackets, J&M PanHard Bar, Barton 2 post short shifter w/bracket, Ford Racing lowering springs, 20x10.5/20x9 Vossen CV3's, JTL Driver and Passenger Side Oil Separators, Sound-tube delete, Redline Elite hood struts, XPEL clear bra, Weather Tech Floor mats, Black 5.0 badges, LED lights throughout, Custom stripes and roof vinyl.