Speed Queen is pretty shallow, but the hoses point straight back near the rear so it requires more depth. Maybe look for brands that the inlet hoses point down under the top panel. Not sure if any are out there like that or not anymore.

Quietest are foreign front loaders, and I personally believe front loaders deal with sand best, keeping grit way from the radial lip seals.

Good luck.

Laundryvet

Out of curiosity, I just measured depth of my Speed Queen 542. It is 28". My own "closet" is deeper than OP's but on-principal I've always used goose-neck connectors to my machines which minimizes hose-flex at the connection points. Additional depth to accommodate the hoses, then, is less than that required for the much larger drain-hose on the machine. I'd have to measure carefully, but I strongly suspect total additional-depth requirement of OP would work.

The dryer's vent-depth allowance would be more troublesome, I would think.

Here is a link that might be useful: Photo of

We have a shallow w/d closet as well. We have the Whirlpool 5300 top loader and (for bi-fold door clearance) the Maytag Centennial dryer with a drop down front door. We thought we would need to pay extra to have the dryer itself side vented, but instead we located the outside vent connection to the side of the machine and used a ductwork extender in the back of the machine. I hope that makes sense. Here is a link to the extender.

Here is a link that might be useful: Vent extender