I’ve heard that what is in the middle of the limb does no work it just holds the tension on the back and
Compression on the belly apart so to speak.
This is mostly correct, but the inner core of the limb isn't doing nothing at all, it is just contributing much less than the wood near the surfaces.
For a rectangular cross section limb the stresses (and strain) are zero at mid thickness and increase linearly to a maximum at the surface, both back and belly. This arrangement means that the majority of the work/energy storage is done in the wood near the back and belly surfaces. For the rectangular cross section it works out that half the work is done in the outer 15% of the limb.
Say you have a limb that is 0.5" thick, 50% of all the work is being done by a strip that is 0.075" thick on the belly and back. The other 50% is done by the 0.35" of wood in the core, which is why I said it doesn't do nothing, but it contributes at a much lower level per ounce of wood.
So What is the fix to compensate for the weaker link?
Possibly by trapping.
Your fix (if there is one) depends on if the early wood is weaker in tension, compression or both. If it is weaker in both then there won't be much you can do aside from lowering the stresses everywhere by making the bow longer and/or wider in the limbs. If it is only weaker in compression then trapping will help by reducing the stresses on the belly. It won't solve the problem but it will improve the situation for any tension strong wood.
Mark