You have to be convinced to stop work on this? I'd have to be convinced to let it keep going...and that's not likely.
Yes. The concrete in the center can have no voids and still be bad concrete. YOU NEED TO TEST IT or better yet, just remove it. You could have already removed and replaced the concrete while you've been screwing around with trying to find answers in this forum that you seem to continue to ignore.
Are your managers just idiots or are they only concerned about costs? There are no specific references that I know of that will tell you that your specific conditions have resulted in bad concrete in the middle, yet there are plent of them that refer to the results of your concrete as problematic. I would point you specifically to the following references:
1. American Concrete Institute (ACI) Manual of Practice (There are similar British and Australian references, so take your pick)
2. Design and Control of Concrete Mixtures, Portland Cement Association
3. Concrete by A.M. Neville (in my opinion, the single best reference available for concrete)
We surmise that you have bad concrete from the poor placement techniques, lack of consolidation, difficult geometry and several other rather clear indicators.
Collectively, the responses you've been given in this thread have amounted to several HUNDRED years of experience, much of which has kept us from being in your position.