Why not just open it sideways? Or, consider a pullout and put items parallel to the front of the fridge?

I'm also 5'8" and I doubt you'll be able to close that cabinet without a step ladder. If I stand in front of my refrigerator and reach up to the cabinet above it, my hand only makes it to the center of the door.

I'm not sure how tall your fridge is but I just have cabinet doors with vertical trav dividers inside. You only have to reach the bottom to open the cabinet and pull thins out. I do have a couple shelves above the dividers for rarely used things - have to use a stool to get to that. I have 42" uppers.

We have a tip up over our fridge and I need a step stool to close it. I'm 5"2" but even so, I think it would be tough to close even for a taller person. We've been trying to come up with some kind of pulley contraption to close it but I'm afraid that even if we could design such a thing, pulling such a large door from one side only would soon cause bigger issues with alignment.

We thoroughly researched so many details for our kitchen cupboards, but when it was recommended by a friend ( cabinet maker and kitchen installer) that a single lift door would look much cleaner than the traditional regular 2 door set up, we just went with it without thinking through the ramifications.

For me, it's not a huge problem as I store rarely used items in that space, not my cookie sheets or cutting boards. But if I could do it again, I would not do a tip up.