I'm glad that you are liking your natural hair. I hope you don't give up too soon and get it relaxed though. It does take some time to get used to natural hair.
Everyone's hair is so different. What works for one person may not work for another, so it may take some time to find a routine/regimen that works for you. Don't give up though, you can do it!
Here are a few suggestions that may help you:
The first thing to do is to try to figure out what is causing your hair to be dry and unhealthy in the first place. Are you under a lot of stress? Are you dehydrated? Are you not getting enough nutrients in your diet? Is your hair over-processed? All of these things have an impact on the health your hair.
If you want to have moisturized hair, you must be hydrated on the inside. Make sure you get at least 8 - 10 glasses of water every single day. Your body is 70 percent water and if you don't drink enough of it, your body will prioritize and send water to the areas that need it most, such as your brain, lungs, and other essential organs. Compared to those organs, your hair is not a priority for hydration. On the other hand, if you're properly hydrated and your essential organs are happy, your body will be happy to send some of that moisture to your hair. I notice that my hair is a lot softer and moisturized when I drink enough water every single day.
You should also think about adding essential fatty acids (EFA's) to your diet. Flaxseeds and flaxseed oil are excellent choices. Udo's 3-6-9 is a balanced essential fatty acid oil. EFA's will help to moisturize your hair from the inside out. They also help to control the production of dandruff.
Heat styling in general is very drying and damaging to your hair. You may want to consider alternate styles to avoid using curling/flat irons altogether.
You'll also want to avoid using too much gel as that can be drying as well.
Have you tried washing your hair using only conditioner? That seems to help a lot with moisture problems. If you're worried about getting your scalp clean, you can add a little baking soda to the conditioner. That really helps. You can do a quick search on the forums to see what other people are saying about that method (I believe it's called the "curly girl" method or the CG method).
DT's are important for dry, damaged hair- at least once or twice per week is ideal. You can use any oil but I really like using virgin coconut oil for DT's because it's not too heavy and washes out of my hair relatively easily compared to heavier oils. Also I've read in several places that coconut oil is the only oil that is able to penetrate the hair cuticle. Apparently it helps to moisturize, condition, and strengthen your hair. You can also use a little coconut oil in you hair on a daily basis. You could try other oils and butters such as jojoba oil, avocado oil, grapeseed oil, shea butter, mango butter, etc to find what works best for your hair. There are of course other recipes for DT's out there that you can try too. I've heard that rhassoul clay is great, but I've never tried it.
How are you liking the Burt's Bee's products? I've never tried them, but if they are working for you, I don't see any reason to change them.
You may also want to think about a leave-in conditioner. I like ABBA's leave in conditioners but there are a lot of other good ones out there. You could have a look at reviews of products in the "products review" section of this site to see others.
I'm not sure what you mean about the balance between protein and moisture....
Ultimately, I believe that healthy hair comes from the inside out. When you focus on having a healthy body, your hair will be healthy too and you won't have to use so many products on your hair to make it healthy.
Hope that helps!