Theo -- I did this recently. Your perspective on the diagrams may be mirror imaged from what the website intended. Just keep an open mind. Verify your tow vehicle's wire functions -- the 7-plug hinged plastic cap has a diagram on mine. Airstream's listed wire color functions for your model-year are quite accurate.
I needed to change the terminal connectors on the trailer end and was aided greatly by bringing an assortment along with a wire stripper/crimper. I found one like this link
at my local fleet store (hardware, Home Depot, etc). You need three size 12-10 and four size 16-14 spade connectors I believe -- but bring spares if Murphy rides along.
We blew a fuse in the truck changing bad running light bulbs with them turned on. Also never test the breakaway switch with a Prodigy brake controller turned on -- it'll fry the brake controller.