Strongly agree with hiding. It's all about preparing the answers to the things that are worrying you.
Your DP needs to show that the episode was specific to a particular time in life, that he got support and that he's thought about it and has made sense of it.
You're on your way with the BMI.
They may probe you about your leave. Can either of you work flexibly after you go back to work, to show that you'll still have time with LO and they won't be in childcare full time?
As others have said, they're really testing the SW, so it's worth looking at any parts of your PAR that feel a bit thin or that might raise questions.
Things they commonly ask are about your support network, how you deal with stress as a couple, how you get support, what sort of child are you looking for and why (because even though it's not matching, they'll approve you for X number of children, up to the age of Y).
Good luck and post again if you need it. I feel for you, having been let down by your SW, but if you don't let the panic get to you, present yourselves as confidently as possible, you should be fine.