Hi Stimmy.
Waking up without back pain is a huge benefit indeed.
Since I’m unable to feel what you feel on a mattress, and you’re unable to describe what it is you’re looking to approximate, I’ll give you this information instead 
which speaks to the different causes of back pain. Hopefully this helps you move in the right direction towards choosing a more adequate mattress:
The most important goal of a suitable mattress is to support the spine and joints in neutral alignment in all your sleeping positions so that the muscles and other tissues can fully relax and not work during the night to maintain good alignment. It also needs enough softness on the surface to allow your pressure points to sink in enough so that direct pressure on various parts of the body don’t cause soreness. Too much firmness or too much softness in either the comfort or support layers can both lead to alignment and pressure issues, discomfort, or pain in various areas of the body.
Lower back issues generally come from a mattress that has upper layers that are too thick and soft and/or support layers which are too soft which can allow the pelvis to sink down too far relative to the rest of the body. This tilts the pelvis which changes the natural curve of the Lumbar spine and can lead to lower back issues. A mattress that is too soft can also allow the hips to sink down too far which flexes the hip joints out of their neutral position which can also lead to joint soreness or back soreness if the muscles are working to keep the back and hips in alignment.
In some cases a mattress that is too firm can also cause lower back issues because the body doesn’t sink in far enough to fill in the gaps in the small of the back and/or the waist (depending on the sleeping position) and the recessed curves of the back can sag. Finally if a mattress is too firm and there are pressure points on the hips (for side sleepers especially) then you may “twist” the lower body away from pressure which twists the spine and and puts it out of rotational alignment which can also cause back discomfort or pain in the area where the spine is twisted.
In most cases … lower back issues come from comfort layers that are too thick and soft and/or support layers that are too soft which can both allow the pelvis to sink down too far and put the lumbar spine out of alignment but this diagram can give you some idea of how mattresses that are too soft or too firm can both lead to alignment issues and back pain or discomfort.
Mid and upper back issues can also come from several sources. In the case of the upper body then good horizontal alignment is important but lateral (side to side) alignment is also important. For example if you bend your head and neck forward towards your stomach and bend the upper body forward into a forward hunched position then it can bend the upper spine and create tension and pain in the mid and upper back. This can happen during the night if your pillow is too high for example and pushes your head forward when you sleep on your back. It can also happen if the upper layers are too thick and soft.
In the same way … if you push your arms and shoulders forward into a forward slouched position then it can also create tension and soreness in your mid or upper back. This can come from a mattress that has comfort layers that are too thick and/or soft and allows your torso to sink in a little too far but “holds up” the lighter shoulders (pushing them forward).
In both cases your muscles will be tense and working throughout the night to maintain alignment.
Upper back issues can also point to a pillow that is either too high or too low for your body type or sleeping position and doesn’t maintain the gap between your head and the mattress and keep your head and neck if good alignment over the course of the night which can affect the upper back as well.
Shoulder and arm issues can come from a mattress that is too firm and puts direct pressure on the shoulders, the shoulder blades, or on the back muscles and can also cause soreness or numbness and tingling in the arms or can often come from postural issues as well. If the mattress is too firm then if you sleep on your side your shoulders may not sink in enough to relieve pressure and your upper body can “twist” away from the pressure so your upper body is “twisted” more forward while the lower body is still on its side. This spinal twisting or torsion can twist the spine in the upper body and lead to soreness in the area of the twist. There is some much more detailed information on shoulder and arm issues in posts #2 and #3 here.
Hip issues for side sleepers especially can be caused by a comfort layer that is too firm or too thin where you can feel the firmness of either the sleeping surface itself or the support layers “through” the comfort layers. These are pressure point issues. In some cases though another reason for hip pain may be a mattress that is too soft which can cause your hips to be out of their neutral alignment and sink down too far which can hyperextend the hip joint and can lead to a burning feeling or pain from joints, muscles, and ligaments that are stretched beyond their neutral alignment. This would more of an alignment issue except instead of spinal alignment it’s about joint alignment.
Trigger points or referred pain. Some people have “trigger points” that can cause pain if they are subject to direct pressure but the pain may be in seemingly unrelated areas of the body that are far away from the trigger point itself. For example some people may have trigger points in their hips that can cause lower back pain or can cause pain that radiates down their legs. While this is more of a medical issue than a mattress issue which is outside the scope of a mattress forum and may require some type of treatment … there is some good information about trigger points on this site and on this site that show diagrams of various trigger points and the areas that they can cause pain and also have some suggestions for alleviating them that can be helpful.
NikkiTMU