Hi jwind,
I think I would probably consider a couple of things if you planned to use the Luroy slatted base.
First it will give you a very low sleeping surface because your bed seems more designed to add a foundation which will raise the height of your sleeping surface by 8" to 9" to a level that is comfortable for most people. If you just use the Luroy your mattress will only come up above the sides of your bed by a few inches and you will have quite a low sleeping surface.
If you do decide to use the Luroy then I would consider adding the Ikea metal side rails (your side rails are wood and seem quite thin) and the center beam but I would measure carefully to make sure that the Luroy will fit snugly without shifting because your bed may not be the same size as the Ikea beds.
Your mattress is thin enough that the Luroy will add some “give” under the mattress that you will probably feel which may make a difference but the sleeping surface itself will be the same and quite firm so it depends on which type of “too firm” you are looking to “correct” (see post #15 here).
It may work well if you are a back sleeper but if you are a side sleeper and you need more pressure relief you may prefer some extra softness on top of the mattress rather than under it (depending on the actual “symptoms” you are experiencing and where they are).
I (and my family) laugh at the same thing … but at least when I do sleep I sleep very well 
Phoenix