I wonder if @NoTengoBattery's custom build will run on that Fritz!box 4040. I have an old release -- about April 2020 -- of his custom build running on my (very similar) Linksys ea6350v3 and it's really awesome; an extremely professional piece of work (and I do management system development for carrier grade network appliances for a living).
It fixes the switch configuration issue and has outstanding performance. I don't use it as my main router because it can only route about a gigabit overall (a HW limitation) and I need more because I have routed internal VLANs, but i use it as my hot spare router just as you describe. Might be worth messaging him or asking in the forum thread.