It's called "Mind-Body," but it should really be called Mind-Feelings-Body. The Mind and Feelings are two separate subtle bodies, along with the physical, that have distinct characteristics. Mind relates to thoughts and beliefs; Feelings relate to emotions. All the bodies affect each other. I see physical illness as primarily caused by the build-up of negativity in the Feeling Body, not because of beliefs held in the Mind.
Then, there are (at least) two kinds of feelings: reactive emotions and core feelings. The reactive emotion is a mostly involuntary reaction to the core feeling, and it can come from the mind, as well as having a base in the Feeling center. Let's say you have a lot of anger about an abandonment experience. The anger is your reaction; it can come from the mind, from the belief that you shouldn't be alone, that you are outraged that you have to go through this experience, etc. Fear, as another example, could be a reactive emotion, or it could actually be a core feeling.
In theory, reactive feelings that come from the mind can be put aside so you can focus on the core feeling behind it. This appears to be what your coaches are saying. If you continue to focus on the reactive anger, to continue that example, you could be spinning your wheels because you're not getting to the core feeling, which is what's mostly responsible for the illness and symptoms. You're in blame, you're worrying, obsessing, and even building the anger. I'm actually curious if there is a school of psychology that you are referencing, because this is a subtle distinction that I wouldn't expect many modern (especially CBT) therapists to understand.
However, in practice, we start with what we have. Often, there is first an awareness of only the reactive emotion. We have anger, but don't see the core. The anger can even obscure the core feeling. So, we start by processing the anger, but - with the understanding that this may be a reactive emotion, and if so, we expect to release it quickly, and then we'll see the core feeling, where we want to devote our main efforts.
There is nothing wrong with processing a reactive emotion in this manner. Don't forget - the EC process includes acceptance and witnessing - key, crucial elements that you have not mentioned. This state is totally different from just thinking about the anger - mulling it over or obsessing over it.
Reactive emotions can build up also, and then they start to become part of the subconscious Feeling Body, so that they may very well need to be acknowledged and some time spent processing them to release the build-up. This is not obsessing, but informed, beneficial inner work.
The emotions you mention are all lower chakra related. They could be reactive emotions, but it's more likely they are connected with your core feelings, because the lower chakras correspond to these feelings. So, I would say you are correct in processing these feelings and not ignoring them, especially since they are so strong. And, of course, it follows they correspond to the lower body issues you mention. So in your case, it looks like the reactive feelings and the core feelings are mostly the same: fear, helplessness, anger (first, second, and third chakras).
With physical pain and illness, our approach is the same as with a reactive emotion. Many times, we don't know the feelings involved, so we start by focusing on the physical SENSATIONS, applying the process and bringing in the healing energies - and - applying witnessing, which is the same as Jon Cabot-Zinn's mindfulness method of handling pain. Once you get the core feeling, you can shift to that, but there is still nothing wrong with continuing to process the body sensations including pain along with the core feeling when working with a physical affliction-core feeling, and I feel it's helpful. That's how I do it with clients. We alternate between them.
Witnessing is the key. You have to keep practicing until you have the experience of what it is. You can't ignore pain, and trying to distract yourself doesn't work that well either. Witnessing and mindfulness are what would be called for, but if you give that a good try and find it's not enough, don't hesitate to use pain meds if you can.