New base or slats for Vispring Bedstead Realm Mattress?

We have a Vispring Bedstead Realm Mattress that we initially ordered in medium tension but switched to soft under the Vispring Comfort Promise. We are both still waking with back pain and have come to the conclusion it must be to do with the bed base.

We have a wooden framed base that is 150 x 200cm that has solid 9cm wide x 3.5cm tall pine slats spaced 7.5cm apart. I have tried placing a 1cm MDF board on top of the slats which helped slightly but not a lot.

I am 5 foot 10 inches (178cm) weighing 12 stone 6 (79kg) and my wife is 5 foot 3 inches (164cm) weighing 9 stone 7 pounds (60kg).

I would be grateful if you could advise whether we need to buy a more suitable set of slats or a new divan base?

I have ready many of your FAQ answers already.
Many thanks.