Awesome!! Looks great. I would recommend packing it down a little bit, for fermentation purposes you don’t want too much air surrounding your cabbage. Can’t tell for sure from the picture but it looks like you might not have salted your cabbage enough, it should be pretty pliable. BTW the chili flake you had was exactly what you want to use for kimchi.
Why no fresh pepper… I imagine it’s a historic issue, kimchi is a preservation item that is made in early winter to last the cold months. At that point in the year fresh chili would not be available. In summer kimchis like water kimchi, you will see some sliced chiles added. But hey this is murca and you add whatever chili you like!
As for the paste, any starch is fine. You often see people use flour, or just regular 'ol rice buzzed with some water in a blender. Really any starch should be fine here as it is intended as food for the bacteria. It’s even fine to just skip it altogether.
As for the gochujang, I think it has too much of a distinct taste for it to work here, your kimchi will taste too much like gochujang. Not that there is anything wrong with gochujang, but it’s not the point of kimchi. It would be like making chili or spaghetti sauce with ketchup. But hey I’m always a fan of culinary experiments and don’t want to discourage you, just know it will become some other thing if you use gochujang.