I am playing High Elves in a tournament. I am thoroughly enjoying it, but I guess my BloodBowl games could be counted on 2 hands, and hence I am not exactly a guru

One thing I am struggling with is the containment of opposition 'Big Guys'. I must at this point say I don't understand why High Elves and Dark Elves don't have access to any, but that is not the point.
What is the point, is how can you contain them? Obviously you can stay away from them by dodging away etc. but is there anything else? For example, the teams I play are:
Khemri (damn, 4 mummies!)
Skaven (not a hitting team, except for that damned Rat Ogre!)
Necromantic (Flesh Golems)
Chaos (Ogres etc.)
Amazons (in the same boat as me!)
Orcs (Ogres etc.)
Chaos Dwarves (Bull Centaurs, Minotaurs etc.)
I know Bull Centaurs and Mummies are not strictly 'Big Guys', but you get the idea.
Any suggestions as to minimisation of their impact would be greatly appreciated. Has anyone had any success trying to outnumber and down them early (in particular the wild animals), or should I simply accept the fact that they will probably blitz or block a player every turn and I will lose players hand over fist?

Thanks,
Brad.