I agree with Cook's Kitchen's comments above. And I think you could accomplish that with some planning. For cupboards you could consider having a browse on Craigslist or Kijiji to see if you can find something that would work for your space.
Or, just get a front load dryer and replace what you've got without trying to stack them which means reconfiguring the space a bit more. Then you could get a piece of counter cut to go across the top of the two machines and that would give you folding space.
I'd get new upper cabinets and go right to the ceiling if you can, that would give you more storage and more workspace on your new counter. That would hopefully mean the stuff piled on top of the cabinets could go inside them instead.
Do you have a Habitat for Humanity restore in your area? Or something comparable? If you kept an eye on their stock you might be able to piece together workable solutions for cupboards and counter. Even if you go to a big box store, a piece of formica type counter (it is soooo much better looking that it used to be) can be had for not a large sum of money. You might even find a gently used front load dryer on Kijiji. A new laundry sink but in the same location and you'd have a nice new area and it would likely be more functional than the current setup.
Then, if you are still bothered by the shut off valves, one of the suggestions above should do it.
Oh....I found some pictures that might give you some ideas.
This is kinda what I was saying. A counter across the top of the two machines, gives you some good space. It is handy to have a hanging rod. This one pictured below is a bit on the small side IMO but still very handy. Those baskets are nice and you can hide lots of clutter in baskets.
This one is nicely done. With the hanging rod under some cupboards that are higher. Imagine if you could find used cupboards in this configuration (from over a stove). A coat of paint and they could look fantastic. Maybe you could find or make a cute little laundry themed sign like in the photo below and hang it so it covers your shut off valves.
I liked this one because they've got a little curtain on the front edge of the sink (easily done with velcro) so that the plumbing and anything else under there - your pails for instance - are out of sight.
Open shelves here and a nice counter over the machines. Easily done and use the baskets to control the clutter.
Q
This is a kitchen in Maryland that combines so many different touches but pulls it off really well!
Q