And a decision made for me too!
If it's of any interest to those in a similar situation, I had quite an extensive travel history, including extended periods in West Africa and the Middle East, but that didn't seem to hold things up (except for them requesting the travel history in the first place, as my background declaration mentioned I'd been travelling). While I spent more than 6 months in some countries, it was never consecutive, so a police certificate wasn't needed.
Best of luck to all those still waiting.