Try jacking the trailer up higher while hooked to the truck before you start to draw up the chains. It won't hurt the truck or trailer at all. You should raise it high enough so that you can easily put the chains on the hook and draw them up. It will seem very odd at first and you will think you are going to break something , but it is fine and is the proper way to do it. If you have an electric tongue jack then the job is almost effortless. The higher you jack, the easier it will be.
If not, then look at it as an opportunity to get a little exercise in before you travel.
Do the same for unlooking also - much safer that way.
You always want the same number of links under tension on each side.
Barney
2004 Sunnybrook Titan 30FKS TT
Hensley "Arrow" 1400# hitch (Sold)
Not towing now.
Former tow vehicles were 2016 Ram 2500 CTD, 2002 Ford F250, 7.3 PSD, 1997 Ram 2500 5.9 gas engine