Having never read MN 39 before, my first impression is we must try to examine precisely for unique aspects.
Therefore, in relation to purity of body, speech & mind, this appears a practise performed communally in relation to other monks. The text says:
Our bodily, verbal & mental conduct will be pure, clear & open,
unbroken & restrained. We will not exalt ourselves nor disparage
others on account of that pure bodily, verbal & mental conduct...
(Thanissaro translation)
You should train like this: ‘Our bodily, verbal & mental behavior will
be pure, clear, open, neither inconsistent nor secretive. And we won’t
glorify ourselves or put others down on account of our pure bodily,
verbal & mental conduct.’ (Sujato translation)
The above appears related to how monks relate to eachother, including making confession to eachother, including for their unwholesome mental states. For example, giving another monk merely a disparaging look would be an example of impure mental conduct. The suttas clearly say monks should look at each other with "loving eyes"; blending like milk & water (MN 31).
“I hope you’re living in harmony, appreciating each other, without
quarreling, blending like milk and water, and regarding each other
with kindly eyes?”
MN 31
Therefore, the above three aspects of 'purity of conduct' appear explicitly separate from the practises described afterwards, such as abandoning the five hindrances. Abandoning the five hindrances may be explicity an "internal" matter/practice; while what is called "purity of conduct" may be an "external" matter related to communal/social conduct.
The above is my impression of the text.
Therefore, 'restraint of the senses' includes when a monk is on alms round and sees a scantly dressed or topless lady, as was/is common in traditional cultures. This example is given (somewhere) in the suttas. This context of practice of restraining the senses on alms round is different to the purity of mental conduct a monk develops towards other monks.
To continue, a monk may be skilled at purity of conduct towards other monks but have sloth & torpor when it comes to personal meditation practice. Thus this monk must develop wakefulness.
The development of jhana is even more distinct. The Buddha himself taught jhana is developed by making 'letting go/surrender' ('vossagga') the meditation object (SN 48.10; end of MN 118). Therefore, a monk may be able to abandon the five hindrances however they may develop a mind of 'rigid imperturbability' ('āneñja') rather than a mind of 'letting go/surrender to the void' ('vossagga').
Note: later texts plus suttas such as SN 12.51 refer to 'imperturbability' ('āneñja') as an non-Noble non-Path mental state.
Also, the development of jhana may not necessarily automatically result in the fruition of the Three Knowledges. The text says:
With his mind thus concentrated, purified, and bright, unblemished,
free from defects, pliant, malleable, steady, and attained to
imperturbability, he directs and inclines it to knowledge of the
recollection of past nivasa (dwellings; abodes; not "lives").
The practice of recollection of past abodes is only fully explained in SN 22.79.
Therefore, the impression of the above is a deliberate act of mind is required to direct the mind towards recollection of past abodes rather than the opposite, which would be to remain in jhana and develop the immaterial spheres.
Note: MN 140 says about the 4th jhana & this step:
One discerns that 'If I were to direct equanimity as pure & bright [of the 4th jhana] as
this towards the dimension of the infinitude of space and to develop
the mind along those lines, that would be fabricated. One discerns
that 'If I were to direct equanimity as pure and bright as this
towards the dimension of the infinitude of consciousness... the
dimension of nothingness... the dimension of neither perception nor
non-perception and to develop the mind along those lines, that would
be fabricated.' One neither fabricates nor mentally fashions for the
sake of becoming or un-becoming. This being the case, one is not
sustained by anything in the world (does not cling to anything in the
world). Unsustained, one is not agitated. Unagitated, one is totally
unbound right within. One discerns that 'Birth is ended, the holy life
fulfilled, the task done. There is nothing further for this world.'
In conclusion, my impressions above show MN 39 may not be a straightforward as it may appear.