My team's output doubled after they started using AI tools and now leadership wants to cut headcount, this is not what I wanted

I manage a team of six analysts. About four months ago I encouraged them to start using AI tools for the parts of their work that were most time-consuming, data summarisation, first draft reports, pulling insights from large document sets. The results were real. Output roughly doubled across the team.

Last month my director used those productivity numbers in a headcount review. The argument was straightforward: if six people are now doing the work of twelve, we only need three. I pushed back but I did not have a strong counter-argument prepared because I had not seen it coming.

I do not regret encouraging my team to use these tools. But I feel responsible for a situation that could cost people their jobs. Has anyone navigated this? How do you make the case that productivity gains should result in more ambitious work rather than fewer people?