I would go about this a different way. Get 3 or more sources connected to an HDMI MATRIX with at least 3 outputs (one for each TV). Connect the Arc to the main TV only. So instead of just switching the audio only, switch both audio and video from one of the non-primary TVs to the primary TV. Since you’re planning on using identical TVs, with the same video characteristics, a fairly simple HDMI matrix will be fine.
If you’re really need to have the audio match the video from the non-pirmary TVs, that I would get something like the HD Fury Arcana along with a HDMI matrx that has 4 HDMI outputs. 3 of those will be for the TVs and 1 will connect to the Arcana which feeds the Arc (You may also need to connect Arcana to a TV for EDID reasons, not sure on that). So now your matrix will control what content is sent to your TVs and your Arc, with all of them playing the same or different sources as you wish.