Welcome to the Gauge. There has been several threads amongst the various forums about keeping cats off of layouts, maybe you can search for them. Unfortunately, the threads usually turn into a juvenile gross-out contest, at which point one or more cat owners get really upset (let's hope this one doesn't). But there might be something useful in them.
Obviously one way is to have the layout in a room that can be closed up, but that's not always possible. We own only one cat (or is it we are owned by only one) which seems to hate the sound of crinkling snack food bags so I put them over the layout while it was in construction. Whenever he got up there he had to step on them and made that awful sound and jumped down immediately. He's never gotten up there since, to my knowledge, and I haven't put anything on the layout for a long time to keep him off.
But each cat has it's own peculiarities, and with six -- jeez! Railery's idea might work out better, if you can make it light enough (would help the dust problem too). You might also check out those transparent vacuum-formed window well covers, probably also available at Home Depot or equivalent, if they're big enough.
ps Don't forget handles!