What you may be overlooking, or what may not be present on your wrench, is the the open wrench is not square to the shaft. It is canted by 1/24 of a circle (15 degrees).
As a result, there's a 30 degree difference between the wrench (normal) and (flipped).
That means you only need a 30 degree arc of motion, not a 60 degree arc. When you run out of travel, remove the wrench, flip it over, raise it 1/12 of a circle (30 degrees), and it will fit on the next flat.
If your range of motion is being compromised by the wrench being all loosy-goosey on the nut (that's a technical term), then you have the wrong size wrench. Do not proceed further because you'll damage the hex corners, which will make the lash problem much worse. In particular, watch out for English vs. Metric. The only wrench sizes that match up are 3/4=19mm, all others will be sloppy.
An adjustable wrench (commonly called a 'monkey wrench', inaccurately) is one answer, but you have to get that tight and might have to retighten on every turn.
It certainly looks like you have more than 30 degrees of motion there (though perhaps not quite 60 degrees). If you are tighter than 30 degrees, first stop and think about how the manufacturer intended this thing to be serviced, because not least, they had to build it and they certainly didn't want their factory workers spending 10 minutes fastening this one thing. If the range of motion is simply impossible, then you need the extreme options offered by others, or perhaps a "stubby" (short length) wrench that allows you to work inside the obstructions...