I assume the vent is through the ceiling? You can used a periscope vent behind the dryer and be able to get a bit closer.
You don't show plumbing, but if you're redoing everything, you can build the hose connections and drain into the wall.
With front loaders, you're still going to have issues with clearances when the doors are open.
The side clearances they're talking about has to do with being able to wiggle the units in and out. You could get by with less. If that wall is not a supporting wall and doesn't have plumbing in it, you might could take it down and shrink it using 2x3s or 2x4s turned sideways.
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vertical storage for linens next to laundry machines
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