SN 47.2 & SN 47.15

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“And how, bhikkhus, is a bhikkhu mindful? Here, bhikkhus, a bhikkhu fetches distinctively (viharati) and contemplates the xxx in the xxx, not letting himself to be defeated (by the fetched phenomena), not distressed (by too much self-mortification,) clearly discerning (that xxx), mindful (putting this event into a remembered dhamma context), having removed the brooding of mischief and evil mind (mano) in regard to the world. 
Kathañca, bhikkhave, bhikkhu sato hoti? Idha, bhikkhave, bhikkhu xxx xxxānupassī viharati ātāpīsampajāno satimā, vineyya loke abhijjhādomanassaṃ
SN 47.2

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Ātāpi in ātāpīsampajāno:

The corresponding BSk. आतापिन् ātāpin = zealous - only appears in the late Lalitavistara Mahayana Sūtra.
I hardly see how it this "zeal" (ardency,) can be applied to Buddha's time.
Therefore, our best shot again is to rely on the Pali and Sanskrit root √ tap.
The Sanskrit √ तप् tap has kept a pre & post Buddha general meaning of "tormenting one's self (like undergoing self-mortification) - to cause oneself pain , trouble , distress - to suffer or feel pain.

Ātāpa [ā + tāpa fr．tap; cp．tāpeti] glow, heat; fig．ardour, keen endeavour, or perhaps better “torturing, mortification".
Tāpeti [Sk．tāpayati - Caus．to tapati] to burn out, scorch, torment.
Tappati [Sk. tapyate, Pass. of tapati] to burn, to be tormented.
Sk. tapati { pr. ac. sg.} of √ tap

Therefore, the meaning of ātāpī seems to be "not tormented" (e.g. by self-mortification) - not distressed. In other words, not in excessive tapas.
Which, in the context of Buddha's time, seems to fit perfectly.

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Sampajāno

Sampajañña: SK. प्रजज्ञान prajñāna [agt. prajñā]
- knowledge , discrimination (AV.)
- a distinctive mark , token of recognition (AV. MBh.)
प्रजज्ञा prajñā [pra-√ jñā]
- to know , understand , discern , distinguish (RV.)
√ जज्ञा jñā
- experience, recognize, ascertain (RV.)

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Sati

A person, on a forum, did translate sati as "putting the events that are contemplated into a remembered dhamma context".
I think this is a perfect definition for sati (sṃrti).
Can't do better.
Perfect.

Therefore, Sati is the nom. sg. sati(mā) in the extract up there. But it is also the all of the process - ātāpi, sampajāno, satimā, etc.
Sati as a whole is "putting the events that are contemplated into a remembered dhamma context" AND "putting the all process into a remembered (sṃrti) dhamma context".

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As far as abhijjhā is concerned, this is how to dig out the meaning:
Abhijjhā [fr. abhi + dhyā （jhāyati），cp. Sk. abhidhyāna]
अभभधध्यस्त्यान abhidhyāna [ abhi-dhyāna ] n.
- desiring , longing for (post Buddhist)
धध्यस्त्यान dhyāna n.
- thought , reflection ChUp. MBh.
धध्यस्त्या dhyā [ dhyāta ] , [ dhyāna ] see under √ [ dhyai ].
√ धध्यस्त्यै dhyai
- to brood mischief against TS.

And Domanassa: (daur+manas+ya)
दौर्मनस्य daurmanasya [ daur-manasya ] n.
दौर् daur
Vṛiddhi of [ dur ] for [ dus ].
दुस् dus
bad (implying evil ), or difficult , hard.
मनस्य manasya
- to have in mind (RV. ChUp.)
Lit. to have "evil" in mind OR to have "difficult" in mind?

In this case, the former - (note: while in jhana four, domanassa has the latter meaning of "difficult").

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Also, the SN 47.15 extract would have the following translation:

“Venerable sir, it would be good if the Blessed One would teach me the Dhamma in brief, so that, having heard the Dhamma from the Blessed One, I might dwell alone, withdrawn (not distracted (alienated) [by the external]), not letting myself be defeated (trampled down [by the distinctively fetched phenomena]), not distressed (by some excessive tapas), and resolute (incited - प्रहित prahita).”
“sādhu me, bhante, bhagavā saṅkhittena dhammaṃ desetu, yamahaṃ bhagavato dhammaṃ sutvā eko vūpakaṭṭho appamatto ātāpī pahitatto vihareyyan”ti.

Appamatto (from appamada).
Appamada comes from pamaddati [pa+mṛd]: to crush down, overcome, defeat.
The Sanskrit √ मृद् mṛd has kept the same meaning from the Śrutas to the Mahabharata = trample down.
Appamada seems to mean "not letting oneself be defeated (trampled down)" - by what is not self - particularly here, the external).

Vūpakaṭṭho - from vavakassati  [v+ava+kṛṣ] to be drawn away，to be distracted or alienated.

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