Wow there's a lot of people on here with absolutely no clue.
I made an account just to say that I relate totally to what you said. I have, on average, a couple cups of tea or coffee a day and have done so for a number of years. I've had problems with anhedonia for a number of years. Within approx. a week of completely cutting out caffeine - reagardless of how slowly I've withdrawn - I fall into the same black, suicidal despair that is only alleviated by more caffeine. I've been stuck in this cycle for a while now - I know it's damaging me but I just can't get off it.
I wish I had answers for you, but I really just wanted to validate your experience. Don't listen to anyone who tells you how you should or shouldn't react to any given substance. We're all so different and can have profoundly different reactions to different things for so many different reasons. Yes, it seems like a rare problem, but no, it's not all in your head. It's physiologically based - we just haven't figured out the cause yet. For me, I know it's an adrenal problem and I think also a gut problem. I thought for a long time that the intense, suicidal Depression was withdrawal and that I just needed to stick it out, but now (after trying many times), I wonder if the caffeine is simply masking the Depression which is always there. If this is the case, I suspect gut health could play a large role. Hopefully you're able to do the cleanse successfully without having to remove the caffeine altogether.
Again, good luck, and ignore anyone who has all the answers.