Computed ultrasound tomography in echo mode (CUTE) allows real-time imaging of the tissue speed of sound (SoS) using handheld ultrasound. The SoS is retrieved by inverting a forward model that relates the spatial distribution of the tissue SoS to echo shift maps detected between varying transmit and receive angles. Despite promising results, in vivo SoS maps often show artifacts due to elevated noise in echo shift maps. To minimize artifacts, we propose a technique where an individual SoS map is reconstructed for each echo shift map separately, as opposed to a single SoS map from all echo shift maps simultaneously. The final SoS map is then obtained as a weighted average over all SoS maps. Due to the partial redundancy between different angle combinations, artifacts that appear only in a subset of the individual maps can be excluded via the averaging weights. We investigate this real-time capable technique in simulations using two numerical phantoms, one with a circular inclusion and one with two layers. Our results demonstrate that the SoS maps reconstructed using the proposed technique are equivalent to the ones using simultaneous reconstruction when considering uncorrupted data but show significantly reduced artifact level for data that are corrupted by noise.