my thought is the laminate is a little too slick to hold the machine in place. Could you try putting some non slip type cushion under? Even the thicker rubber pad used as laminate pad may work, or the non slip padding used under area rugs. It would be a simple fix if it works.

Where is the washer located? What is below it? I mean.... is there a basement or crawl space below? If so, try putting a pole from the basement (or crawlspace) floor to the floor joists under the washer. What your washer is sitting on must be very solid. Floor joists that span 12 to 14 feet can have a lot of bounce in them. Once the floor joists are moving it exaggerates the vibration of the washer. It's not your flooring material choice in any way shape or form. Don't cut your flooring. Whoever told you that is an idiot. This is a STRUCTURAL issue. I don't mean structural FAULT... there's nothing wrong with your house except some architect that doesn't have a laundry area on regular flooring and didn't design the proper support into it. This is normal. You need to take the bounce out of the floor STRUCTURE, not the floor covering.

I have that exact same desk! I bought it at Pier One in the early 90's. It's been in 3 homes with me, one in the Netherlands. Good score!!!

I use Blick Gallery frames for the art in my husbands office. These open easily in the back. I use thick ones, so cut pieces of foam board to take up the excess space and use an acid free mat. I also use a thin piece of acid free foam board behind the print. They are very economical and very simple in style. They might be too simple compared with the frames you have now, but that may work with your new home style and give you time to slowly reframe your art. If your art is mostly framed prints, opening the back and changing out the mat is not difficult in many cases.