Prepopulate an entity reference in an inline entity form
I tend to use CER (Corresponding Entity References) for things like this. 

As an added benefit, you can hide the reference field on specification_text_section giving a slightly cleaner editor experience.

I have a couple of similar setups where I have IEFs on the grandparent, parent, and child, so you can create all 3 from any level and CER handles reverse reference. So, if I create a parent node, I have 2 IEFs, one for the grandparent and child, but don't show the field referencing the parent in either IEF forms.