Hi fraggle,
Unfortunately back pain is usually an indication of a mattress that is too soft under the pelvis which is allowing your pelvic girdle to sink down too far which in turn puts the spine out of alignment. If this is the case then it’s not not really possible to effectively “fix” a mattress that is too soft because it would normally require either making the support core firmer or removing the comfort layers and making them either thinner or firmer.
There are some ideas in post #4 here that may be worth trying and if you have an actual box spring that flexes (as opposed to a foundation that has no flex) then it may be worth trying your mattress on a firm non flexing surface (such as the floor) to see if it helps as well. if this makes a difference then you could purchase a firm non flexing foundation.
You can also see a “home made” alternative to the mattress remedy that one of the members put together in post #9 here.
Phoenix