Hi sleeplessonlatex,
Your mattress would be a fair bit firmer than most side sleepers would do best with and it’s unlikely that it will “break in” enough to be a suitable match for you because latex doesn’t soften as much as other types of foam materials.
There are some suggestions in post #2 here that may be helpful but the odds are high that a topper (or a mattress exchange) would be your best solution.
Having said that … lower back pain is usually an indication of a sleeping system that is too soft and by choosing a topper that is that soft (14 ILD is a very low ILD) and 3" thick (which is fairly thick) you may have overcompensated and exchanged one issue (a mattress that is too firm) with a different one (your mattress/topper combination is now too soft). With your higher weight this would tend to affect you more than your wife.
I certainly wouldn’t be concerned with the durability or longevity of a latex mattress or how much it would soften … with or without a topper … because latex is the most durable of all the foam materials and I would choose a mattress that is as close to your ideal as possible when you test it rather than buying a mattress that is too firm with the intent of adding a topper (see post #2 here).
Based on your feedback … “in theory” the 36ILD core with the 24 ILD comfort layer (you didn’t mention it’s thickness) would probably be a better choice that would move both of you closer towards a more suitable firmness range than the mattress you currently have but if I was in your shoes and you have the option available I would return to the store and do some very careful testing on the mattress (using the testing guidelines in the tutorial post and with both of you on the mattress) so that you can use the results of your testing and what your body tells you to make the best decision because the most reliable way to know which mattress (or mattress/topper combination) is the best “match” for you is based on your own personal testing and/or experience.
If you find that you still need a little more softness after that then you could use the information in post #2 here and the topper guidelines it links to to help you decide on the firmness and thickness of a topper that would have the best chance of success.
Phoenix