We don't currently qualify for the SS grant but I'm going to try and see if we can once the baby is here as our wages go up/down depending on how much money the company makes (and no offence to DH but I probably make around 2/3 of it at present!), so income is going to drop like mad come December. From what I've heard you can try and claim for it for up to 3 months (or maybe 1 month? not sure) after the baby's come, so I think that's the best time as you can know exactly what you're getting mat pay wise and how much the household is earning.
It's a long shot but from what I've read on other forums, it depends on the sob story you can give them, some people get it when they don't even need it, so it's worth a go.