Got the platinum today.
I used the method explained by spiddel, just focus on 3 and 5 reps contracts.
My best advice is to focus on 3 reps investigations with a silver-silver-gold or silver-gold reward.
I got my last 5 crowns just doing this in less than 5 hours.
I needed big nergi, small and big teostra and kushala.
I even got both crowns for teostra on the same investigation (if i remember, a silver-silver-gold-gold 2 players 0 death allowed -the best possible ??-).
Big nergi and both kushala were silver-silver-gold.
If you dont have that type of investigation, try to find an SOS flare, its worth a try instead of farming 5 reps contracts.
Just do the same for normal monsters.
To make it clear, if you want to get a black diablo, its better to farm a silver-silver-gold investigation on pink rathian (black diablo should be on the map aswell) than farming worse contracts.
When you farm, you should be able to notice when a monster is big, small or average. It saves a lot of time if you abandon quest, go back to camp when you're not interested.
But some of them are harder to measure properly and you should kill them all if you have any doubt. I had the most difficulties for lavasioth/juryatodus, radobaan/uragaan and diablos.
EDIT: i can confirm gold crown from 5 reps investigations. But you should not prioritize them. Use them to understand how to measure a monster (belly, head, legs and knee ?), get more investigations, etc.