I would! FWIW- love my Electrolux ventless dryer. Going on 3y and no issues.

Side vent the dryer thru the wall into the garage and up the wall in the garage and out thru the roof.

Cabinets on the wall over the washer, dryer and sink. Put a deep sink in a base cabinet.

If you want to put the laundry in the pantry, you'll have to open up the wall and install doors in a wide opening. If that wall is load bearing, then there are more i$$uses to deal with.

Personally, I would rather have the wide open laundry area that you already have. Plenty of room to sort the dirty clothes onto the floor and the ability to close the door on any messes in there. Lots of potential there to better organize the space and gain a lot of storage.

Do the washer and dryer in the mudroom back up against the pantry? What kind of foundation do you have? Depending on your foundation, relocating water and drain lines varies from really expensive to astronomical in cost.

"Side vent the dryer thru the wall into the garage and up the wall in the garage and out thru the roof."

I had thought about venting through the room then realized by the time that's done I wouldn't be cutting the vent run down by much - back to square one with vent issues.

"If you want to put the laundry in the pantry, you'll have to open up the wall and install doors in a wide opening."

Why would I have to open up the fall if I can fit the appliance through the existing door?

"Do the washer and dryer in the mudroom back up against the pantry? What kind of foundation do you have?"

No, they back up to the foyer. Have a partial basement; not sure if the mudroom has basement underneath or slab - I'd have to figure out the end points of the side rooms in the basement.

Why would I have to open up the fall if I can fit the appliance through the existing door?

IF you can get both appliances into the pantry (and I don't think that it is possible to do with the existing door opening), then you need room in front of the appliances so you can operate them.

My laundry 'closet' is 53.5" deep with a 40" door opening and I know how restrictive that is. If I had only 45" of depth, I don't think the dryer door would open. I have conventional old school appliances. 29" wide dryer with fold down door & skinny Speed Queen top loader (<26" wide).

...realized by the time that's done I wouldn't be cutting the vent run down by much...

Would venting the dryer through the roof eliminate any elbows? Do you have rigid (smooth) ducting or is it all flex vent? What is the length of the current run vs the thru-the-wall & Up option? Keep in mind that heated air rises so you'll gain some venting help when the vent goes vertical. Thru the wall and up will require just one elbow and possibly another 120 degree fitting (if you need to offset because of a wall extending above the roof of the garage. In calculating vent length equivalents, an elbow is equal to 5' of straight run length. So, if your current set-up has more than one elbow, you may be gaining more efficiency than you realize. If you have a lot of corrugated, flex duct, you'll benefit by replacing with smooth rigid venting.

My venting scenario is awful. I had 4 elbows in about 12' of run. We were able to switch out one elbow for a 120 and replaced most of the flex w/ rigid duct. Still far from ideal but those changes made a significant difference in drying time. Even heavy loads like jeans (out of the SQ top loader) dry with one setting of the dryer (about 50 minutes.) Most other loads dry in 40 minutes. Synthetic loads in much less time. Before, I routinely timed out and had to reset the dryer a second time in order to get dry clothes.

The suggestion to to go through the roof is pretty solid. Vertical venting has it's drawbacks, but probably fewer than you currently have.

If you have to tunnel under the foundation to run new plumbing, You could probably buy a nice compact Bosch stackable washer and condenser dryer, small dehumidifier, and have cabinets built for the cost of plumbing alone.

A floor plan would be helpful in determining if there are other options you might consider. From what I’ve read, you’d be fine with a washer/dryer closet so, you should have someone look at your house and determine if that is possible and what it would cost. Personally, I would rather finish the existing laundry area and add a countertop and deep storage over the machines and sink. That won’t address your coat/boot storage needs very well though.

What is behind the wall across from your washer and dryer now? If you could steal a bit of space from there, and move your garage door closer to the washer, you might get enough room for a long closet. A bit pricey but you’d have a gorgeous laundry/mudroom.

This might inspire you.

I had similar needs, in my laundry/mudroom. In the end, I opted not to expand into the garage (behind right wall) to build a closet but, as I have extra tile and the room below is open, it is a decision I can revisit. Honestly though, I am so much happier with how this room looks and functions, because I’ve added storage and an area for boots, that I’m not missing the closet nearly as much as I thought I would. There are coat hooks for each of us in here or we just walk the few extra steps and hang our coats in the entry closet.

I talked to DH about it, and he nixed the idea of moving the machines to the closet. He did make a comment that gave me a lightbulb moment -- I honestly don't remember what he said, but whatever it was, "move the door!" popped into my head. That's it! If I move the two doors (one to the kitchen area, the other out into the garage), it will open up space along the entire wall opposite the machines since right now the doors abut the wall. If I move the doors, I can put 18-24" cabinets, area for shoes and coats, etc. I'd have to go with the ventless dryer due to the compact size and the fact you can get them close to the wall in order to move the doors enough to allow for meaningful storage space, but that should work. I talked to a friend's husband who works in the building trades, and he said since I have a ranch it should be a fairly straightforward job for a contractor.