You might find it easier to go with a compact washer.

Home Depot has this LG that might work for you.

https://www.homedepot.com/p/LG-Electronics-2-3-cu-ft-High-Efficiency-Compact-Front-Load-Washer-in-White-ENERGY-STAR-WM1388HW/207024938

With a compact washer, you could add a couple sheets of 3/4" plywood to the washer side of your shelf. That would bring the top of the washer close to the level of the top of your dryer. Home Depot, Lowe's, etc. will cut for free a sheet of plywood for you into panels with the dimensions you need.
Or, you could put the plywood on the dryer side to raise your current dryer to the height of a new full-size front load washer.

In your other post, you mentioned being in Chicago and liking ABT for appliances. The LG compact is back-ordered at ABT and a lot of other places. Also, when I looked at this model last spring as a possible replacement for my 2008 Frigidiare Gallery front load washer, I found a lot of reviews and comments about the LG WM13888 doing a very good job but working best with small loads and needing twice as long to run cycles as our Frigidiarie Gallery front loaders do. For a speedier and more capacious compact front load model, you might look at the 2.4 cu. ft. Electrolux EFLS210 , which seems to be in stock at ABT. (FWIW, that was going to be my choice for replacing my 2008 Frigidiare Gallery until I found an easy fix that cured my old Frigidaire's problem.)

For a full size replacement washer, have a look at the newly released LG WM3600 which does seem to be in stock at ABT, does allow adding items to a wash in progress, For even more basic washers, you could check out the just-discontinued LG WM3500 or its replacement, the WM3400. (Odd that the new model has a lower number, but LG seems to have replaced the WM 3500 by bracketing it with the WM3600 and WM3400.)

For capable but basic full-size front loaders, you also might want to look at Electrolux's ELFW317 which also is in stock at ABT. Georgect probably knows as much as anybody here about Electrolux washers and maybe could comment on that as a choice for a basic, full size front load model.

Corrected my post above --- the LG WM3600 does not have the turbo-wash system which makes for speedier washes. (Apparently, the WM 3600 is replacing the WM 3700). For that, you have to get the soon-to-be discontinued WM 3900 or its successor model, the WM 4000. Both are listed as "in stock" at ABT and both seem to be sale priced below your $1k budget cap but maybe still more than you want to spend.

Thanks, jwvideo. I'm also trying to find a new mattress, so am scattered with decision-making. I appreciate your input!