An inexpensive way to get a hefty base board is to use 1"x6" boards and a 1 3/8" base cap. It will be nearly 7" tall and it's an easy install. I would use a 1x 3/4" base shoe with that but that's a matter of taste. The base board provides the visual foundation for the room. As such, it's the one piece of molding that can be out sized compared to the rest. Get some of the material you intend to use and lean it against the wall in your room and see if the size works. If you feel that your existing case should be larger a backband is an inexpensive way to add some size. You'll need a table saw for this but if you have one or can get to one it's easy after that. Take some 1"x6" and cut it into strips 1/8" wider than your case is tall. Sand the banding and break the leading edge with sand paper. Install it around the outside of your exisitng casing. When it's finished you'll gain 3/4" in width and extra depth. Visually it will appear even larger. I've never used foam crown but it could work. The trim in commercial buildings is commonly glued on foam. Once it's painted who's to know or care? They used to make it out of plaster even cement and nobody cares. I can't imagine how your crown molding is going to get dented. If you try it report back on how ti went; I'd like to know.

When I had my kitchen renovated a few years ago, I was in a bit of a dilemma: to add additional crown molding to the rest of the kitchen or not. I had simple Shaker style cabinets installed and decided to not have additional crown molding installed in my kitchen. I like the more minimalist look❣️

What is meant by "likely 8 ft"; do you not know the door height that was ordered? What is meant by "Casing can’t be adjusted but maybe it can"? You describe the moulding as a crown but show a cove. IMO the cove is much too large and a crown might be better. Get some smaller cove and crown samples and mock up the door and ceiling trim until you find a good compromise. This shoud be a visual rather than a math exercise.

5" for windows I think would be to wide. For base ok. Gee did I do something wrong since my window trim on my second floor with 9' ceilings is a 1 x 6 or 5.5" wide. Oh well. BTW: My base on my second floor is a 1 x 8 or 7.5" high. For the OP, I'd do the standard on the second floor and upgrade to the 5" just for the first floor base since money is an issue. Personally, I'd skip the crown for now and add it later if needed. As others have stated, you don't want your base to be the same width as the windows and door trim. The base should be larger than those.