Are these DSP's best for this kind of Active noise cancellation for rigid barriers?

Me and my partner have been looking at many of your DSP's Eval boards to use for our Active Noise Cancelation (ANC) Senior design project. We are trying to stay under $250, just for the DSP Eval board, maybe higher if needed. They're a few forums that show people using the ADAU1452 Eval for their ANC design but I've seen people that say they had problems with the latency not being fast enough when using the 1452.... Is there a different DSP that you might recommend that would result in less latency, as the signal needs to travel from the Ref/Error mics (no more than 1ft apart since they will be against walls, on the inside and outside of the same wall), then signal goes to mic pre amps, loudness comparator, then mic path selector, then the ADC to DSP to DAC..., then push-pull amplifier, and finally the transducers... Adding attachment to see design.

I know the ADAU1452 Eval (and most of the others) have an ADC and DAC on the board but we are anticipating latency, due to our research on this kind of design and using this DSP, so we found the ( CS4271-CZZ Stereo Codec) IC and was also wondering if these are the good option to help lower the latency, but we also want to know if they will even work with any of the ADAU DSP's since those IC's are 3rd party, or should we stick with the ones on the board?

This is becoming a long question, so if anything, the MAIN focus of my Question is mainly focused on if this DSP will work and if not which would be the next best option (ADAU1452, or 62, 66, 72, 78.... or anything else you have) that you would recommend for this type feedforward method of ANC (even if it cost more I'd like to know which one and why if possible, if its less expensive then thats even better!)

Any advice at all would be extremely helpful. Please see the attachment as I am hoping that will hopefully help in recommending the right DSP for this project.
Thanks so much in advance for any help.

P.S.
This is probably a bad question so I apologize in advance if it is, I am totally new here, but are the over seas versions of these kind of DSP 1452, 66 etc... boards on Ebay or Aliexpress not worth the risk? Thanks again!

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Audio Signal Processors

adau1452

ADAU1778

anc

Feedforward ANC

Active Noise Cancelation

adau1463

SigmaDSP Audio Processors

adau1462

adau1466

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