First some half-meandring information on your idea, go to "long story short" for the answer.
Because DNA continuously breaks down and might not always be available, its also relatively slow.
Thought processes are complex (citation needed), and yours are one based on a quarternary calculation system. But its not just one DNA sequence doing the work, its millions doing sequences and parts of calculations that monitor the body, its surroundings, collect data to form idea's on what it should be doing and how, which muscle groups to activate and what sequences, stored data that needs accessing to recognize what is present in the surroundings and to apply previous experiences and current mood and tasks of the creature to come to a conclusion. So you need a robust system that can correct a few errors on-the-fly.
Unfortunately DNA isnt that flexible. It's incapsulated in the ribosomes and communicates by splitting partially at the right spot, generating messenger RNA (I think it was called that) which then transports itself through the ribosomes and... somehow through a process we dont understand and seems to be based on random chance to eventually reach its destination... reaches the right parts of the cell at some point to have the cell perform its tasks. This complicates matters enormously: first something has to get into the cell and to the DNA to pass the information it needs to start its calculations. After the calculations it needs to generate RNA in order to communicate its answer, and hope it moves to the edges of the cell fast enough to get the next Cell's DNA in line to start the right calculations, hoping its the right cell and that the surrounding cells process their messages in a timely fashion as well despite the randomness involved. (Note: I tried looking but neither my textbooks nor the internet actually mentions how a cell processes information, they all focus on the transmitting between neurons. I cant find if the process takes place in the main body or the dendrites, or that it uses electrical or chemical processes to process its information before it sends it on. I have no idea why that gap is there and it drives me crazy).
On top of that, when a cell is dividing the DNA is duplicating and unavailable (unless like neurons it does not divide and relies on a type of stemcell for replacements), and DNA degrades over time with use and divisions. The body does try to repair it but even when it successfully does so that part of the DNA has created faulty results that needed to be corrected, and eventually these cells will have too many DNA faults and break down/be terminated by the body and replaced.
Long story short:
Your creatures use neurons to send the information, but have a data processing system that is great for long-term thoughts and planning but not that handy for quick short-term thinking. So when these creatures activate their bloodlust and get to killing things it takes too long for their brain to tell it to stop again. Under duress the amount of information the DNA has to process in quick succession will cause information loss and information mingling as the RNA will not always arrive at the cell body's edges and be send on in the same order that they were generated.