Hi senza201,
There are two reasons that a mattress can sag which is either the materials or components in the mattress or the support system under the mattress.
From the description of your bedframe it sounds like you have a bedframe and isn’t designed to directly support a mattress without a foundation on top of it.
You’ve probably read this already but the first post of this topic here has more information about the types of support systems that are generally suitable for different types of mattresses and some good sources for each of them. If your mattress is all latex (which it may not be … but you can check on the law tag to see if there are any other materials in the mattress besides latex) then you would need a support system with little to no flex that has a center beam with good center support to the floor and no more than 3" of spacing between the slats.
I would agree that the first thing I would do is put your mattress on the floor to see if this solves the problem (which it should if the only cause of your sagging is the support system under your mattress and not the materials in the mattress). If it does then you will need a good foundation (not a box spring with springs inside it that flex) on your bedframe and under your mattress. I don’t think that a bed beam will provide the type of support you are looking for although it may still be a good idea to improve the strength of the support underneath the foundation.
If height is an issue and you don’t want the additional height of a typical foundation or even a low profile foundation then a slat conversion kit like this may be a good alternative to a thicker foundation.
If there is still sagging in your mattress when you have it on the floor or with a suitable foundation underneath it then the issue may be the materials in your mattress and some of the suggestions in post #4 here may be helpful but the first step I would take is to put the mattress on the floor to see if this resolves your situation.
Phoenix