Hi marcandre,
Tracking down the cause of back pain can involve a lot of detective work and in some cases some trial and error because there are so many possible variables involved. As any health professional who deals with back issues can tell you, it is among the most complex of all symptoms to deal with and sometimes the cause of the pain can be in a different area than the symptoms themselves and it can take a lot of time and attention to fine detail to zero in on the cause.
In the case of a mattress … back pain is usually a symptom of some kind of an alignment issue. This could either be from one part of your body sinking in too far or not enough relative to the rest so that your spine is not in it’s neutral alignment, it could be from sleeping in a twisted position, it could be from sleeping in a more rounded or hunched position, it could be that the natural curvature of your spine is somehow different from the norm (poor “learned” posture over time or just a natural difference in your makeup) or it could be that your body has a “learned” sleeping memory from another mattress that is different from the one you are sleeping on now and it needs time for stiffened muscles and ligaments to loosen and relax and for the body to get used to the new sleeping surface … even if it is better and more appropriate for you in the long term than the old one.
One of the complications of this is that there are dozens of variations in sleeping positions and combinations which affects the pressure distribution along the body surface and how the body responds when it is sleeping. Sometimes too the “range” of natural alignment for some people is very narrow which means that even small changes in any direction can cause issues while others with more flexibility may have a wider range of neutral alignment and sleep well on almost anything.
So the first thing to do is to establish a base point with the original mattress which means to make sure you have slept on it for long enough that your “symptoms” show a consistent pattern which isn’t changing (either improving or getting worse over time). This usually takes several weeks becuse the body will also be adjusting to a new sleeping surface during this time. Once you have a clear pattern that has “stabilized” and isn’t changing any more … then the key is to make any changes in small increments in the most likely direction of improvement and see what effect each change may have in an effort to track down the underlying cause of the pain. I would also talk with the manufacturer so that you can use any expertise they may have and their greater knowledge of the material combinations they use in their mattresses to see if they have any suggestions.
So step one is to describe the exact layering of a particular combination … describe the combinations of sleeping positions you have during the course of the night in more detail … and to describe the exact position and nature of the pain or discomfort you are having.
Once you have slept on a particular combination for long enough to confirm that there is a consistent pattern then this experience is used to make the next change that has the best chance of improving the symptoms and then the process repeats. Any symptoms that come from this new combination as well as any changes in the symptoms between the first and second combination can then be used to “point to” any further changes that may be needed.
So in essence … its a narrowing down process of slow incremental steps involving a combination of different factors including the mattress layers, your symptoms on each, the adjustment process of your body, and the details of how each new layering produces changes in your “symptoms” that may help point to the next step.
So your original mattress was …
5" HR foam ILD 38, 1" latex 32 ild, 2" latex 15 ild.
On this combination what was the nature, type, and position of your pain?
Could you also describe the combination of sleeping positions that are most typical for you over the course of the night (in as much detail as possible rather than just the generic “side, back, stomach”)?
Do you have any tendencies for back pain at any other time?
Anything else that may be helpful?
One clue is that on the futon (which I assume is very firm and has no real “comfoft layers”) … it appears that you had back pain only rarely. Did you sleep in the same combination of positions on the futon or do you find yourself sleeping in different positions on your new mattress? When did you typically have back pain on your futon on those occasions when it did happen? Do you still have the futon as a source for “experimentation”?
Are your layers loose so you can use any combination you wish (which seems to be the case). If this is the case … have you tried a “bottom up” approach such as just the 5" of HR foam with an inch of the 32 ILD latex and did this change anything. The “bottom up approach” involves starting with the layering that produces better alignment (but may involve pressure issues and won’t be as comfortable as you would want) and then slowly trying comfort layers that improve pressure relief without compromising alignment (or cause twisting or any of the other possible causes of your pain and discomfort).
One step at a time 
Phoenix