In our case we were the first employed couple to apply. The "Dr" in front of DH's name usually helps too.

Forget the mat leave bit. Just say that your income IS what it will be. You're back at work fairly soon, aren't you? And you've got the letter from your employer, I don't think it will be a big deal.

We have managed to land some fairly in-demand places over the years, we are those annoying people who snap up places as soon as they're listed. We offer all of these: start paying rent immediately; to pay 5-10% more than the asking rent; will pay 6 or 12 months upfront if it will help us secure the place. And we always call the day after we submit the application.