I should also note that the GC would prefer to keep the toilet against the existing wall of the house (easier to run the plumbing) and the dryer on the outside wall, so he can vent through the wall to the outside.

9x9 seems pretty tight...our mud room/laundry room is a little less than 9x9 and we have washer, dryer, freezer on one wall, broom closet, coat closet and bench with cubbies above and baskets below on the other wall. Doors on opposite ends. The guest bath is in the next room at about 5x5. 30' makes a long space so you may want to put some function on the other side of your doorway and get all the functions in.

I think you need to lay it out to see if it will work. Block out a vanity that is at least 22" deep, an elongated toilet, and the largest washer and dryer that you can find and see how much space that leaves you.

I have a very small house that has a tiny powder room (3.5' x 5') a small master bath (4.5' x 8') and a closet for my washer and dryer. One of my frustrations is that I cannot buy "normal" appliances and fixtures. Front-load washers won't fit in my laundry closet; I have to go with the top-loader and not even the largest top-loader. One bathroom can only accommodate a 16" deep vanity and the other only an 18" deep vanity. Both can only take a round toilet. Remodeling has been frustrating as I have a lot fewer choices and often they are more expensive.

I have a 1/2 bath and a laundry room/mud room in 6'x12.5' space. The bath is 6'x4.5' with the toilet and sink along the 4.5' wall. The laundry room / mud room takes of the rest of the space (about 6'x8'). When I remodeled, I switched to a stacked, front loading, high efficiency, large capacity washer and dryer. So far I love it. They don't take up much space (about 3' wide) and so the rest of the space (about 5') is used for storage, sorting, etc. The laundry room / mud room is also a pass through to the garage, so it is fairly heavily trafficked. While I'd love to have a massive luxurious laundry room with room for clothes drying racks and linen storage, I simply do not have the space. What we do have works well for us.

What about something like this?

You could put some mudroom type cubbies on the opposite wall of the addition.