What do you think about mandatory berserking if the rating difference is e.g. >500 points?
This sounds plausible, 500 points is enough to make berserk mandatory. On the other hand, how about give a piece odds if the difference on rating is higher than X?
I actually don't mind playing normal games without berserk/odds, but since you ask the question at the end of the post, I thought I'd chip in and give some options.
To give a piece odds is a good idea, but hard to manage. One need to start from a different position etc. Too complicate in practice to administer and control the adherence of it.