You have to be very gentle trying to move that 4x4 shifter - it WILL bend the shift fork inside the trans. I replaced a couple of them on mine over the years. You just have to be patient and move slightly back & forth from forward to reverse with LIGHT pressure on the shifter. Turning the steering wheel has absolutely nothing to do with the difficulty and will not help.
You have to drain the hydraulic oil and remove the cover from the left side of the trans that holds the shift fork assy to inspect the fork. The fork simply slides a small gear that is on the shaft that runs all the way from the rear differential up to and just out of the front trans where the external driveshaft connects and goes to the front diff. This gear is very simple with no syncronizer and engages to a gear that is part of the rear diff pinion shaft. That long internal driveshaft is supported by a small, $6 bearing (from NAPA) in the rear diff housing right next to the pinion shaft. If this bearing is worn or damaged too much the two gears won't engage/disengage easily or at all. I had to do a rear split on mine years ago to replace that bearing. That's what taught me to be VERY careful when shifting the 4x4. I had to heat and bend my 4x4 shifter to keep my left leg from resting against it while operating the tractor to keep from bending shift forks and haven't had to replace one in years now.
I also don't run on any pavement anymore so mine stays in 4x4 ALL the time now and it has worked well for years now, contrary to what some will say about that. My tractor is a 2001 model and has almost 3200 hrs. on it.