It most certainly can be unnerving sitting in tree stands. Standing on something the size of a pizza box 20 plus feet in the air has a way of doing that. You will get comfortable with it as long as you develop trust with your safety harnesses.
You want a harness that has a linesman belt connection on it as well as the between the shoulders drop connection. It must have been a big tree for your tree strap not to be able to go around it, or a short tree strap. I connect my linesman belt around the tree backwards once I’m standing on the platform as well as the drop strap above my head, I feel very safe like this. This gives me more confidence when I stand up because I can lean out against the connected linesman belt, it can limit your side to side movement though.
I connect my drop strap so that when I’m sitting on the seat and lean out a bit, it becomes tight. I usually sit leaning out a bit against that strap support because it’s comfortable and reduces fatigue. Cabelas has a tree strap that is a great item for climbing up to your stand very safely once it’s set up without having to undo the linesman belt all the time to go over tree branches. You just slide the prussic knot along as you climb. This type of tree strap is left attached to the tree after the stand is set up. Do a search on the U.S. cabelas.com for “prussic”. This useful item is the treestand lifeline. Because its left attached to the tree after you’ve left your stand it can be stolen by lowlifes.
As you probably know, make sure your screw in tree steps or branches always allow you to step down onto your platform. I like lots of branches so I almost always select spruce/pine trees for my stands.
To lift my stand up into the tree I use a small pulley with an eyelet at the top of it. Can tire sells them for a few bucks. I tie a rope around the stand laying on the ground then climb up the tree with the other end of the rope. Tie the eyelet of the pulley to a tree branch or screw in foot step above your head then run the end of the rope from the stand through the pulley and hoist the stand up. Once you have the stand generally up to where you want it you can tie off the pulley rope and deal with it safely without having to hang onto the weight of the stand. A linesman belt wrapped around the tree is a must when first setting up the stand so that you have both hands free.
Be safe up there, tree stands are dangerous. I don’t want to give the coyotes a chance to chew on my carcass.