Going full component wouldn’t be required; you could very well keep your Famicom hooked up to AV1, and then run your PS1 and PS3 through a component switcher into AV2.
Alternatively, you could spend a little more to get a SCART switcher and an RGB SCART cable for your PS1 so your Famicom and PS1 are hooked up to AV1, and then connect your PS3 to AV2.
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