Chrono Gallery - Scoring

I thought of a potentially better scoring system for Chrono Gallery: Museum of Lost History. I am liking the sound of it more and more as I talk about it and refine it.
Rather than scoring at the end of the game for particular sets, and rather than having to put your tiles into 3 distinct exhibits, perhaps instead there could be 7 Trophies:

• Most of any Culture
  
• Most Tools
  
• Most Weapons
  
• Most Art (should this be "Sculpture" instead?)
  
• Most Ancient artifacts
  
• Most Medieval artifacts
  
• Most Modern artifacts
  

As soon as you qualify, you claim one of these trophies and hold it until someone outdoes you by having more of that type of thing than you do. So if I have 3 Tools, I claim the Most Tools trophy to indicate that I have the most impressive Tools exhibit. If someone else gets 4 Tools, they have a more impressive Tool exhibit than me, so they take the trophy from me.

Whoever has the most trophies at the end of the game has the most impressive museum and wins the game. Or maybe trophies are worth 2vp apiece, so that certain tiles could be worth 1vp or something.

I think this scoring system has a lot of potential. I do sort of miss the idea of having to decide which artifacts to display, so I have a possible additional constraint idea...

Maybe each player can only display like 6 artifacts at a time, and when winning a new one, if you want to keep it, you must discard one you already have. The trophy tiles or cards could indicate their qualification requirement on them, and when you qualify for a trophy, you claim it. Then you flip it over to the back side which indicates a more stringent qualification condition, which a player must meet in order to usurp that trophy from you. Thus, you go for a trophy, claim it, then go for some other trophy. Due to the nature of artifacts having 3 attributes, you could potentially get another trophy without much additional work!