Static hedge for one over a clamped stock price

A claim pays $1/\min(\max(S_T,K_1),K_2)$ at expiry, where $K_1<K_2$: that is $1/K_1$ below $K_1$, $1/S_T$ between the strikes and $1/K_2$ above $K_2$. Construct a hedge from vanilla options that works whatever model the stock follows.

A bond plus calls weighted by the payoff's curvature. Using $f(S)=f(K_1)+f'(K_1^+)(S-K_1)^++\int_{K_1}^{K_2}f''(K)(S-K)^+dK+\ldots$, hold bonds paying $1/K_1$, short $1/K_1^2$ calls at $K_1$, a strip of calls with density $2/K^3$ for $K\in(K_1,K_2)$, and long $1/K_2^2$ calls at $K_2$ to flatten the payoff. In practice the strip is discretised.