Are the Seven Factors of Enlightenment understood to happen as specific phases in a linear progression in one's journey or are they understood to happen in a circular manner with ever deepening understanding?
I like to teach them as linear, but it's not really that simple. The Buddha said (SN 46.53) that when the mind is agitated you should cultivate the last three (tranquility, concentration and equanimity), and when the mind is sluggish, the second through fourth(investigation of dhammas, effort and rapture):
"At such times, monks, as the mind is sluggish, that is the wrong time to cultivate the enlightenment-factor of tranquillity, the enlightenment-factor of concentration, the enlightenment-factor of equanimity. What is the reason? A sluggish mind is hard to arouse by these factors.
"Monks, when the mind is agitated, that is the wrong time to cultivate the enlightenment-factors of investigation-of-states, of energy, of rapture. Why? An agitated mind is hard to calm through these factors.
Mindfulness, the Buddha notes, is to be always cultivated:
"But as for mindfulness, monks, I declare that it is always useful."
If we will be able to free our minds from other external objectives and concentrate on the Satara Satipatthāna (The four foundations of mindfulness), if one could do it, then it is the Sapta Bojjañga (the Seven Factors of Enlightenment) that is going to get developed in him. That is, the items that aid attaining realization will start to get developed in him. There are seven items that aid realization.
Sati (mindfulness) Dhammavicaya (investigating the Dhamma) Viriya (effort; energy) Pīti (happiness) Passaddi (tranquility) Samādhi (concentration) Upēkkā (equanimity)
We will start to understand that cultivation little by little (Sati). When a mind concentrate on the Dhamma in this manner, one will develop the talent of investigating the Dhamma by his wisdom (Dhammavicaya). When the talent of investigating Dhamma by his mind is developed, his effort gets cultivated (Viriya). When effort is developed, happiness gets cultivated (Pīti). When happiness is formed, alleviation/tranquility with respect to his (physical) body and mind gets cultivated (Passaddi). When he feels that relaxation with respect to his body and mind, his mind gets concentrated (Samādhi). A concentrated mind will become temperate since it is cultivated by wisdom (Upēkkā). This mind we have can be cultivated to that level. So with the purification of one factor helps achieving the same for the next factor. At the same time it is not strictly a linear process. Take the following as an example.
Proper Concentration (Samma Samadhi) is one of the 7 factors of enlightenment (bojjhanga), and one of the five spiritual abilities and powers (bala). Concentration the last link of the 8-fold path. In the 3-fold division of the 8-fold path morality, concentration and understanding, it is a collective name for the three last links of the path. Proper samadhi has the qualities of purity, clarity, stability, calmness, readiness, and gentleness. It is perfected in one-pointedness (ekaggata). The supreme samadhi is the one-pointed mind (ekaggata-citta) which has Nibbana as its sole concern. In a broader sense, samadhi can be translated "meditation," meaning development of the mind through the power of samadhi. A very good sutta that fully explains of this Supreme Samadhi is Rathavinãta Sutta. It explains in full the seven purifications (SAPTHA VISUDDHI) taught by the Buddha. Try to understand what these seven purifications are, that is found in the Rathavinãta Sutta (M.I,145).