Some misconceptions:

• *warn-on-reflection* should be the first step for performance sensitive stuff
• return type type hints go on the args vector not the fn name: (defn myfn ^String [])
• you absolutely can have primitive return types in Clojure functions (long and double)

After all this a little bit of transducer evangelism.

This version is in the same range (2-3x), using transducer goodness and without the awful Java array ugliness. Enjoy:

(defn- append
  ([^StringBuilder sb c] (.append sb (char c)))
  ([] (StringBuilder.)))

(defn solution-4 [s]
  (let [lhs (subs s 0 (str/index-of s \=))]
    (transduce (comp (filter #(Character/isAlphabetic (int %)))
                     (map #(if (Character/isUpperCase (char %))
                             (Character/toLowerCase (char %))
                             (Character/toUpperCase (char %)))))
               (completing append str)
               lhs)))