You should probably rent a laser level to KNOW the correct degree of angle you truly have to start with, end with.
You really can’t tell level by looking. Features of the ground and dirt, where you stand, can fool your eyes pretty easily.
We put our barn on a raised pad area. It has been truly helpful in draining the volumes of rain water the roof collects, along with putting barn ABOVE the ground height for flooding. None of the flood water has gotten close to the barn doors because they are raised. This stays true during really heavy rainfall, 6" in a couple hours. Over 12" of water in a short time, plus the added drainage water from higher surrounding areas coming to fill our drainage ditches as water leaves. Makes you glad to live on the high side of the river!!
I know you want to save money, but how you build the “under pinnings” of your barn is a big deal. Drainage, both natural with the raised pad, French drains around the outside barn walls, leading roof water away, can make your barn fun to live with or a constant headache with mud inside and out.
I would definitely hire the work done, they KNOW how to move things because of much practice. They are good with angles, drainage of land surfaces because they have done a lot of it. Watching the guys come here to fix our drain tiles was amazing. They were so smooth, got things done quickly. We got excellent results in drainage and how the top surface looked when refilled. They made it look like it was such easy work! I have well over 40 hours with my tractor in ONLY moving dirt piles, leveling and smoothing things. I still have a lot to learn to be even close to a “good” earth mover.
Gravel pits often offer earth moving services. Lots of local contractors or small operations will work small jobs for you. Ask around for good contractor names that do good work.