The description of science given is that of the Newtonian understanding of physics and chemistry. Scientists like Einstein, Bohr, Schrodinger, Feynman overturned this "mechanical" perspective.
For example, the "sequencing" of which you speak does not apply to the quantum level, where effects can precede cause. On the other side of the scale, in cosmology, time itself is not an independent entity, and past, present & future are completely dependent on the location and velocity of the observer and the observed (General theory of relativity).
Science does not "contain controversies". There are many questions that science currently does not have a theory for, primarily because we lack observational data. In this case, scientists will have no problem saying "we don't know (yet)". There is no shame or controversy in this.
As for the interchangeability of mass and energy, you must realize the amount of energy required to create matter is staggering and beyond human capacity to even imagine.
Science has made great strides in the field of neurology in the last decades. Quantum brain dynamics (QBD) is a recent hypothesis to explain the function of the brain within the framework of quantum field theory. Since quantum theory is the most fundamental theory of matter that is currently available, it is a legitimate question to ask whether quantum theory can help us to understand consciousness. Observations have identified quanta of long-range coherent waves within and between brain cells, and showed a possible mechanism of memory storage and retrieval in terms of Nambu–Goldstone bosons.
The implication is that subjective experiences of all kinds, including experiences of subtle energies, are secondary to, and derivative of, objective, physical processes.
Where science is based on objective observation, Buddhism is experiential. Vīrya (Sanskrit; Pāli: viriya) is a Buddhist term commonly translated as "energy", but it has nothing to do with the concept of energy in physics. To discuss the relation between the concept of energy in Buddhism versus physics, we must differentiate:
- energy as a primary attribute of the objective, physical world,
- energy as a secondary attribute of the subjective, sensory world, and
- a nondual contemplative view of energy in the world of experience.
Many contemplative traditions of the world, including Buddhism, have sought to understand a unified world of experience, which includes a spectrum of subjective and objective phenomena, with no absolute division within this spectrum. Within this world of experience emerged the Greek concept of pneuma, Indian prana, Tibetan loong, Chinese qi, Japanese ki, and Native American mana in their respective medical traditions, all of which are supposedly present in the body and the environment at large.
In Buddhism, the energies coursing through the human body are investigated from a first-person perspective by first honing the attention by means of sophisticated contemplative training. Therefore, the Buddhist view has no objective, quantitative means of examining energy. And since we know that the quantum level very likely plays a role in the brain, the uncertainty principle & the observer effect virtually make it impossible for a contemplative discipline to make 100% accurate predictions and assertions.