You've gotten a lot of great advice, and probably the best is going back to what you were using without irritation, and slowly changing one thing at a time. It probably seems obvious now, but changing everything all at once can make finding the problem impossible. Give Proraso's sensitive-skin soap a try while still using Harry's carts, and Maggard's synthetic brushes. They are inexpensive and extremely high-quality, just like all of Maggard's stuff. Rosacea runs in my family so animal-hair brushes can be a bit of a game of roulette, but I can really scrub the daylights out of my face with those synth brushes.
Depending on how sensitive your rosacea is, you could also be sensitive to some of the ingredients in your gear. Here is an amazing aftershave and face balm recipe: equal parts ALCOHOL-FREE witch hazel, 99% pure aloe, and a few drops of vegetable glycerin to your liking. Shake it like a polaroid picture, then put it on everything except the dog. If you are feeling adventurous or there is an essential oil you like, you can add a couple drops of that for some fragrance.
Depending on how sensitive your rosacea is, you could also be sensitive to some of the ingredients in your gear. Here is an amazing aftershave and face balm recipe: equal parts ALCOHOL-FREE witch hazel, 99% pure aloe, and a few drops of vegetable glycerin to your liking. Shake it like a polaroid picture, then put it on everything except the dog. If you are feeling adventurous or there is an essential oil you like, you can add a couple drops of that for some fragrance.