If the bench is too low, build it up with sand bags or something to make it comfortable, not tolerable. Some extra shoulder padding may eliminate the fear on getting cut with the scope.
Take your time getting things the way you want them, then and only then will you truly enjoy the range, and achieve your best performance.

Find a copy of "The Accurate Rifle" by Warren Paige. He'll take you thru bench technique. Without proper technique, the bench is valueless.

A newer book that will help is "The Ultimate In Rifle Accuracy" by Glenn Newick. He also has a chapter on bench technique.

Both books are aimed at the bench shooter but both have a chapter on the hunting rifle also. Paige's is better in my opinion.

I just bought a "lead slead" and it picks the whole operation up about 16" off the bench

I've had similar experences over the years. In my profession and with hunting rigs I now shoot from a supported prone position. I found that it can be just as steady and your whole body helps soak up the recoil. Best of luck.

I have also found that when at the range the benches are too low or chair too high. In any case I took a 2x4's and cut into 2 about 14" long and nailed them sid by side on a 1/2" sheet of plywood then cut plywood to match. I put my vice on this to raise it up when on low benches. You could also make it larger as needed and put sand bags on it. Its really helped me out. I will usually use this set up when zeroing a gun or doing a zero recheck. Otherwise I offhand, sit or prone shoot.
A piece of advice I was given some time ago was clamp my gun in the vise adjust it so scope is dead center. Rather than hold the gun use my free hand to hold the vice down. Look through the scope and ensure sight is on center and pull trigger, never really griping the stock or puting my cheek on it. NOTE either gun needs to be lower cal. or very secure in vice so it don't jump out. By doing this I have found that I'm not moveing the gun at all with natural body twitches. My zero groups are much better. Doing this with muzzle loader seem far more productive when working new loads and distance checks. I have a decent notural body twitch so it help me.

I'm with csummerall. I bought a lead sled about a year ago, and I never sight in with out it. It's great on recoil. I can put by 416 rem in it, and it's comparable to shooting an -06. Also, a lead sled will really help insure that you are placing the cross hairs in the same spot when you're sighting in. It'll give you that extra height as well. I had the same problem b/c I'm 6'3". I actually got scope gapped the first time I shot a 300 weatherby, but now I can shoot my 416 remy or 338winny w/a scope and w/out any problems.

What kind of gun/cal are you shooting, and how long is the barrel? Shorter barrels pop up more, and it's always a good idea to hold them down at the front when shooting off the bench.

The sled, or sand bags are really important so that you don't develop the dreaded flinch. Good luck.

Ive found that when using the lead slead it pretty much takes the human out of the equation and sighting in is super fast even with a new shooter or gun