When Can I move Kittens?

My cat gave birth just over 2 weeks ago. Mum and babies are doing great, but she gave birth under my bed. It's a very low bed and the only way I can check on babies is by lifting the mattress, but I'm almost 30weeks pregnant and it's becoming a struggle. The current box is very shallow, about 5-8cm tall (I had to cut it down so that it would fit under the bed) with one side dropped down, but as the babies are starting to walk, I thought they'd probably need a taller box soon. Plus, as I said I'm almost 30 weeks pregnant and lifting the mattress to check they're doing okay, eating and pooping properly, is becoming a struggle. I've tried moving her and babies into a covered, larger box in the alcove of my room, with a cutout so she can climb out safely but babies wont be able to climb out for some time. Since the room is literally only occupied at night, it's very quiet all day, but she just moves them back under the bed.

I'm not really sure what the best course of action is. Please help?!