Hmm, good question. It depends on how we define a caravan stage. *usually* they are timed, and the parodius da special mode isn't. But it does have other pillars of caravan stages - that is to say multiple paths and things to shoot to reveal score stuff. So it is ultimately a score attack mode, with a limited scope, which is perhaps more important than being timed?
I think I'll add an "almost caravan" section and put that in there
And to Black Tiger's point... boss rush is a bit further from the edge for me, so I think it requires its own category again. it does have little things you can hit for more points, though!