I finally bought something that works! Having abandoned the idea of a cheap SCART switcher I picked up a BT945
. This meant that (a) I can plug 5 things in at once (b) it takes the Gamecube's component inputs rather than needing a SCART convertor (c)I can have two separate outputs - one for Ed's room (via a remote sender) and one for mine and (d) it treats the widescreen signal properly, which means that switching from the Tivo to the DVD player puts my TV into widescreen (if I'm watching a widescreen DVD).
And it all worked perfectly first time!
I must remember to stop buying the cheapest option, save up and go for the one that actually does what I want in the first place. I'd save so much time and stress.