To weigh in here on the pepper front. I've been growing, using, etc peppers for a very long time (well for me, lol) and I've found the best way to ensure that they stay fresh is this. Dried peppers *do not like humidity* ... period... they tend to rot. Acidic based preservation yields the best results. And for the majority of those preservation methods, it's vinegar. Which we know can and most likely will affect the end cheese flavor/consistency/etc. What I think is the best answer to this, just from a pepper stand point is fresh.
Why I say that is this. Cheese matures to a natural acidic balance over time. That is the right environment to retard bad mold growth and degradation. What I think is key here is the right pepper, and the right mixing of flavors.
I agree 100 percent by previous posters that a spicy pepper cheese really needs to taste a specific way. It needs a mild flow of flavors mixed with the occasional *pow* of pepper flavor. To achieve this you really should either pre cook them, which makes them mushy and not as fun as fresh, or perform an alcohol extract of dried flavors that you add to your cheese. An alcohol solution, ie, white lightning, will extract an incredible significant amount of flavor and capsicum. If you were to say add that extract into a fresh whey solution, coupled with the fresh pepper chunks, it is this persons opinion you would achieve the overall desired flavor.
The question here is how does an alcohol extract affect the chemical composition of cheese.
That is something I don't know.
What I would try is this. Take one dozen Jalapeno's... dry them in a way similar to jerky... any dehydrator will do. A tip here is to make an X cut on the end to facilitate faster drying. After that, take a coffee bean grinder, I have one for peppers, and one for coffee beans. Grind them up into a fine powder, seeds and all. Place the entire contents into a sealable container, usually a mason jar and fill with at least 1-2 inches above the powder level worth of white lightning alcohol. You can use lower potency alcohol for flavor, but for a pure extract white lightning is the best. Wait several weeks for the process to complete. The liquid left is an incredibly potent pure extract of the flavor of the pepper.
Couple that procedure with your original fresh pepper cuttings and I'll bet you 100 bucks it's going to deliver on taste. What I would caution however is the amount of extract to put in. That 1-2 inches in that mason jar will last a very long time. I would start off with 1/4 tsp amounts to 1 gallon at first and judge it's effectiveness. Increasing it over time to discover what the flavor level you want.
I could talk peppers for ever, lol... I should probably hush now.