I think your pepper is getting too much calcium, to be honest. Calcium and nitrogen are supposed to be in balance, I believe. Too much calcium and too little nitrogen could actually give the appearance of calcium deficiency. I know I've had plenty of blossom end rot on tomatoes that had loads of calcium, and hardly any nitrogen. Adding extra nitrogen may be helpful to curb the symptoms, and to help in the composting of the wood chips (if they're not fully composted), but I think the safer solution here is to repot it in a mixture without so many wood chips throughout the soil. Wood chips on top as mulch are probably fine.
I'm not really sure how much nitrogen to recommend adding, but probably more than usual. Not only should calcium be in balance, but if your wood chips aren't composted enough, the bacteria need nitrogen to aid in their decomposition; so, that could increase your requirements.
Doing a foliar spray with nitrogen might be particularly helpful, since it shouldn't be lost to the bacteria that way. I wouldn't add more than is usual for a foliar spray (just if you put it in the soil).
Since you mentioned calcium nitrate, be warned that it's toxic, though. So, don't get any on yourself. Don't inhale it. Don't get it in your eyes. It can kill microbes, too. It even seemed to deter aphids when I fertilized peppers with it once. However, I don't think adding more calcium to the soil is what you should do. Calcium nitrate as a foliar spray might be good, but it's hard to say. I'd use other nitrogen unless you like to experiment.
Now, keep in mind, I could be wrong. So, be careful. Maybe the soil had plenty of nitrogen already added. These are just my guesses based on the evidence.