It sounds like the most constructive innovation you could implement, as Keith implied, is a review of how your company goes about setting objectives. Forgive me if I'm reading too much into it, but your question sounds a little bit like "Quick! Be innovative!"

But HR, these days, is a data-driven, evidence-based discipline and we shouldn't be doing things purely for the sake of wanting to be doing what all the cool companies are doing.

You should have a breakdown of HR's expenditure in the last FY. Look at whatever's largest and work out what you could have done to make it smaller. It could be as simply as re-negotiating a contract or changing a contracted provider.