I use a KitchenAid Mixer for my bread making, entirely. I used to love doing it by hand, until the KitchenAid took over my kitchen...now it does everything I can possibly get it to do--so, I don't think the mixer is your likely problem. I do have the dough hook on quite a bit longer--perhaps a total of 7 minutes, and I usually have the machine knead the dough on medium (4 -5) speed.
People usually refridgerate their dough for 1) increasing the flavor or 2) b/c they have time to make the dough now and time to bake it tomorrow or the next day. Your recipe has the dough sitting out for about 10 minutes? That's not enough. Dough will rise more slowly in a refridgerator--it will still rise, I've had freezer bags of dough bust from it rising in the fridge--but in order to have the dough be light and airy, you really need to get it to room temp if you are going to refridgerate it. That will take at least an hour, depending on the temperature of your home.
Sometimes, when I am in a bit of a hurry, I will preheat my oven to its lowest temp, about 165/170, and then shut the oven and place the dough in the oven to warm it up from the fridge. You have to keep your eye on it, but this will work.
Someone else mentioned, I think, that you only have one rising here, and its in the fridge. I agree, the dough should be risen and and reshaped, then allow it to rise in its pan.
I always tell people to make sure you put an oven thermometer in the oven. I was surprised at how far off my temp was, and it was causing problems with my baking that I hadn't attributed to it. But I suspect allowing the rising to occur, as said above, so it doubles in size and rises over the top of the pan, will help.
I also use instant yeast, much easier, and I check that I am not getting the water too warm--no hotter than 110, or the yeast will die.
And yes, that's a heck of a lot of flour and I've never made bread with that much yeast (or salt). Try halving the recipe.
You can overrise too, so keep an eye on it! Overrising will result in the bread falling and--accckkk!--dense bread.
What the heck, even dense, warm bread is great with butter and jam :)
Practice, it gets better. And here's a website I like too Welcome to the Fresh Loaf | The Fresh Loaf