According to the text, The Antagonist gets 1 Strife when defeating a Hero in a simple contest. Is this 1 strife per hero defeated in that contest, or 1 strife per contest, as long as at least 1 hero is defeated?

Whichever is the case, I worry about the potential for Strife-harvesting here. Simple probability leads me to anticipate that the GM will be able to get 1 or more Strife in the majority of contests, even if he leaves the difficulty at 2d6. (Assuming 3 or more players anyway.)
Also, imagine how much strife a GM could harvest from creating ridiculously diffocult contest like, say, 2d12. Not as much as the contest costs, certainly, but enough to ffset the actual cost. That 7 points might actually work out only at 3 when 4 heroes have failed their rolls (if it's 1 per hero).

So should they be a set cost for calling a contest? Should this Strife award be abolished? Am I worrying too much?

It's 1 Strife for each Hero that loses the contest (rolls lower than the Antagonist).

And yes, I think you're worrying too much. :)

Remember, when the Antagonist makes the 2d12 contest, she is automatically giving one of the Heroes 7 Glory. Getting a few points of Strife back in return is no big deal.

Also, the Strife budget is really more of a pacing mechanism. The players are not playing against the Antagonist! They're playing against each other. "Too much strife" has never been an issue in the dozens of games I've played so far.

John wrote:
Remember, when the Antagonist makes the 2d12 contest, she is automatically giving one of the Heroes 7 Glory.

Not quite! Success or failure doesn't matter. The highest rolling hero -- win or lose -- gets the extra Glory, according to the table on page 117. Beating the Antagonist is a seperate issue, and is worth 1 Glory.

Hmmmmmm. Another little error on my part.
Cool.