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The binary neutron star coalescence GW170817 was observed by gravitational wave detectors during the inspiral phase but sensitivity in the 1-5 kHz band was insufficient to observe the expected nuclear matter signature of the merger itself, and the process of black hole formation. This provides strong motivation for improving 1--5 kHz sensitivity which is currently limited by photon shot noise. Resonant enhancement by signal recycling normally improves the signal to noise ratio at the expense of bandwidth. The concept of optomechanical white light signal recycling (WLSR) has been proposed, but all schemes to date have been reliant on the development of suitable ultra-low mechanical loss components. Here for the first time we show demonstrated optomechanical resonator structures that meet the loss requirements for a WLSR interferometer with strain sensitivity below 10$^{-24}$ Hz$^{-1/2}$ at a few kHz. Experimental data for two resonators are combined with analytic models of 4km interferometers similar to LIGO, to demonstrate sensitivity enhancement across a much broader band of neutron star coalescence frequencies than dual-recycled Fabry-Perot Michelson detectors of the same length. One candidate resonator is a silicon nitride membrane acoustically isolated from the environment by a phononic crystal. The other is a single-crystal quartz lens that supports bulk acoustic longitudinal waves. Optical power requirements could prefer the membrane resonator, although the bulk acoustic wave resonator gives somewhat better thermal noise performance. Both could be implemented as add-on components to existing detectors.