Interesting question. I haven't read anybody else's response yet, but here's what springs to my mind:
I'm not sure I agree with your definitions of higher-end and fast fashion. For example, my Brooks Brothers shirts, for which I paid quite a bit less than $200, are very nice quality and not at all what I'd call fast fashion. They have classic styling, good quality fabric, great construction, and I bought them with the intention of wearing them for a long time. You certainly can spend more than $200 on a good shirt, but still. You don't need to. But on the other hand, for something like a blazer, you're certainly going to spend more than $200 for higher-end.
Anyway, let's forget about the dollar threshold for high-end for a sec. I think we can all agree that a $7 pair of pants from the Gap counts as fast fashion. Do I have anything like that in my closet? No. I expect my jeans to last. I've got lots -- they're important wardrobe staple for me. I don't consider any of my jeans fast fashion.
I think, if we're looking at jeans, shoes, and coats and jackets, ALL my items qualify as higher-end (but not super-high end, designer wear). It always pays to spend more there (except maybe for jeans; you can probably get good ones for less than $100). With tops, it's more like 25% higher-end, 75% mid-range. I have nothing "cheap" at all, mainly because I'm too old to get away with cheap construction and flimsy fabrics, and also because I'm a careful, selective shopper. But I haven't had to replace an entire wardrobe all at once, like you do! To answer your question -- how to build an entirely new wardrobe by winter -- I would recommend spending more on nice footwear and outerwear/jackets/blazers, and buying good-enough stuff for the rest, which can then slowly be replaced as you see fit.