Are you storing the bales all on one level? Or are you going to have to stack them in order to store the quantity you need?
With a proper counter balance no the back ( grading box or bush hog ) you may be able to lift the bales enough to clear the trailer and SLOWLY drive them to their location as long as you don’t need to lift them more than 18" off the ground.
If you find that the bales are too large for your tractor to lift intact, then I would open the bale and lay 1/4-1/3 of the bale onto ratchet straps. You can then “retie” the bale and move it. The nice thing about these bales is that they are baled sooooo tightly that they tend to want to stay together even though the strings have been cut.
The first time I tested using these types of bales, I put a pallet in the back of my truck. I had the farmer load the bale onto the pallet. The bale overhung the pallet by a bit. I secured the bale to the bed of the truck and left the tailgate down. Once I was home, I put a wide wheel barrow at the end of the tail gate and cut the hay strings. I peeled flakes off until it was within the length the forks on the tractor to manage getting to the pallet. Once at that point, I retied the strings by making a loop at one end of the string and then making a loop at a point along the other string that I could double back to and use the 2 loops as a pulley system to tighten the bale to ensure it wouldn’t fall apart.
I am storing my years worth of XXL hay bales on pallets covered by tarps. I had originally built my barn thinking I would use small squares and store most of a years worth of hay in the loft. The cost difference ($600 worth of XXL squares or $1600 worth of small squares) was such that I didn’t feel that I could justify staying with small squares. If my horses have no grazing, they eat 1 to 1.5 flake(s) of an XXL bale a day.