Well the World Cup issue is just because JKR sucks at math. For the sake of ease it's probably best to assume from 1994. So yeah, there would be a tournament in 1998 I'd imagine the UK didn't compete because of the war but that'll have to be left up to the modly ones. If we want to go from 1473 then the cup would be next year, which is what I was going on because it makes more sense.
Either way I doubt the UK would have played in 97 or 98.
But here is the thing about that tournament, it's got a long ass time of play before the final teams are determined. I don't remember if its said specifically in GOF (and I don't have them here to check) but its implied that England lost several months before to be knocked out of the tournament in just the semi-finals. That leads me to believe that the process of getting to the tournament would take months, if not an entire season.
But the European Cup is discussed in Quidditch Through The Ages, usually that is used as a supplement to canon but if we aren't going to go that way here then yeah we could just make some random game (or just do that anyway). I'd assume with the European Cup that it'd be the same team as for the World Cup barring players who were injured etc and needed to be replaced. Teams playing on that high level would need time to work together and train, so I just don't think they'd throw a team together at the end of a quidditch season with roughly three weeks to go or something.
I know they do that at the Olympics, but the result is usually a hot mess.