Solutions for uncomfortable divan bed

[Elliegeez]

I have a divan double bed and I love how it looks. I needed 4 drawers and struggled to afford to buy one. I found this one on Amazon for a very good price and fell in love with how it looked. The problem is that I like how it looks, sleeping on it is another matter.
The top of the divan is not completely flat. It came in 2 halves and where the halves meet, it raises slightly. This is exactly where my hip is when I lay down and I end up with a stiff back most mornings. It also seems to dip slightly in the middle of the 2 halves.
I can't afford to replace it (divans with 4 drawers seem to be ridiculously expensive) I spent £100 on "bunkie boards" that go under the mattress but they came in 3 separate slats that sit horizontally, meaning that the middle slat sits on the raised section. It's better than it was but still not great.
Would I be better off buying 2 thick MDF sheets to put vertically under the mattress or perhaps getting a thin memory foam mattress underneath? Or if you have any other cheap solutions, I'd be very grateful.

Can you put something thin under the ends of the two halves so that they are the same height as the middle bit? Maybe try a bit of spare carpet or a thin board?
If not then your board plan sounds good. I would go for some plywood because it will be stronger. You don't need it to that thick. 10mm should do. If you buy from somewhere like b and q they can cut it to size for you. I would put some extra bits under it where the gaps are so that it is supported properly otherwise it will just bend over time so it ends up saggy in the middle.