As stairs to the basement drop, the space over is called "headroom". To figure out how much headroom you have at any point along a staircase, multiply the number of steps you have gone down by the riser height of your staircase then subtract the thickness of the flooring, floor joists, and ceiling sheetrock. Here is a diagram to help... Typically you will need to have about 11 steps down before you have sufficient headroom to stand upright. In your diagram above, you could definitely turn the storage area into a utility room and use the current utility room area for a mud room with a door between the two located next to the garage wall. There would definitely be plenty of headroom beneath the floor by that point. The spot RIGHT where you have the words "stair line" would likely have a sloped floor but it would probably only extend about 2 feet into that space so you could put a regular height countertop and a false front cabinet there and use it as a drop zone. Alternatively, you could just continue the stairs on towards the right another 4 or so steps and put the landing beneath where the word "Work" in workbench is. If you waited to make the stairs turn until you reached that point, you could turn the entire utility/storage area into one big mudroom/laundryroom and not worry about sloping floors anywhere. Probably wouldn't want to put the washer and and dryer into the corner where the "workbench currently is" because of the need for drainpipes. But other than that, you'd have a free hand. Of course, this would change how the basement rooms would have to be set up but... Then again, depending on how you plan to use your basement and how easy you want access to it from the main floor of the house to be, there is yet another possibility. That is, turn the stairs around by 180 degrees and start them over where the work bench is. By the time they reached the hall, you would have plenty of headroom. You could probably even shift that little closet toward the garage so that it sits over the stairs tho it would have a sloped floor. But, you could put angled shoe storage on the sloped closet floor and make a positive use of that space.

Personally, I would want a door to close off the laundry room from the rest of the house. Next, I would want to access the 1/2 bath without having to enter the laundry room. You might want to use it when guests come or larger groups and I wouldn't want them having to go through the laundry. Absolutely, you need a sink.,,,hand washing, mop buckets, wet towels, etc. I have a huge double sink....one side for dog washing the other for chores. I'd want an area to hang laundry out of the wash. I would also want a lot of counter space for folding, wrapping presents, crafts, etc. Where would you put your ironing board?

Your laundry/mud/bath is a similar layout to what I have, except I have a tub/shower in that bath. A laundry setup like that doesn't leave you much storage, or room for ironing, folding, or hanging, so keep that in mind. I have to do my ironing in my bedroom. I also don't have a utility sink, to make room for extra cabinets. While a utility sink would be great, I do have a kitchen and bathroom sink close enough that it's not a big deal. And the way the rest of that floor is played out, it puts that bath really far from your guest entrance, office, living room and dining room. You mentioned a downside being that guests will walk through the mudroom, but remember that they will also have to go through your kitchen to get to the bathroom. I'm not sure I'd like that. BTW, you might as well forget about the door between the kitchen a mud room, as it will almost always be open. We changed ours to a cased opening instead of an actual door. I'd have preferred to go with a pocket door, just in case we wanted to be able to close it off for some odd reason, but we didn't want to have to tear into the wall to do it.

Thank you for the comments and suggestions. I would like to address a couple things. Our eat-in area is sufficient for 10 people. I have custom built in benches and a table in he nook area. If I went ahead with the plan to close the dining room, I could always use the open office space across the foyer. It doesn’t lend itself to “office” work anyway. Our front walk is quiet long with a side entry garage, this is the reason most people don’t use the front door. If I were to have a formal occasion, I would certainly close the garage and have people enter this way. However, we very rarely have any formal guests or gatherings that would call for the formal dining room or formal entry. My laundry/mudroom area is very small and there’s no room for style as is (washer/dryer) cabinet for some cleaning supplies. I should also point out, this house has no extra closet space, meaning the closets in the bedrooms are it...no linen closet, utility closet, nothing. Right now, any mop, broom, vacuum, etc are in the spare bedroom closet and in the corner of the tiny pantry. I’m just trying to maximize my kitchen area without having to change the kitchen. I thought a butler’s pantry/entry could do that. I see that I should possibly look at other options.