I think DN 15 offers som criteria for narrowing down the meaning of upādāna in the context of dependent origination (DO). Excerpt:
It was said: ‘With wanting (taṇhā) as condition there is upādāna.’ How that is so, Ānanda, should be understood in this way: If there were absolutely and utterly no wanting of any kind anywhere—that is, no wanting for visible forms, wanting for sounds, wanting for smells, wanting for tastes, wanting for tangibles, or wanting for mental objects—then, in the complete absence of wanting, with the cessation of craving, would upādāna be discerned?” “Certainly not, venerable sir.”
“It was said: ‘With upādāna as condition there is existence (bhava).’ How that is so, Ānanda, should be understood in this way: If there were absolutely and utterly no upādāna of any kind anywhere—that is, no kāmupādānaṃ, diṭṭhupādānaṃ, sīlabbatupādānaṃ, or attavādupādānaṃ—then, in the complete absence of upādāna, with the cessation of upādāna, would existence be discerned?” “Certainly not, venerable sir.”
Upādāna is constrained from two sides: One one hand, if you don’t want anything you don’t have upādāna. So it should be possible to deduce from a translation of upādāna that no wanting means that upādāna can’t exist.
On the other hand, no upādāna means there can’t be bhava (which I here take to mean rebirth as Ven. @sunyo suggested earlier in the thread). So it should be possible to deduce no upādāna means no rebirth from the translation.
It seems to me that in order to take a new rebirth, this new existence has to have some content, there has to be something to play around with, there has to be a source of energy to drive it. If there was no upādāna – no sense pleasures, no views, no ideas of a self – there’d be nothing to draw one into a new life. There’d be nothing to do.
I think maybe one has to resort to a combination of take up, take in, draw on and draw in to capture the aspect of appropriation but also consuming the objects of appropriation in the process.
Going back the analogies:
“Suppose, friend Ānanda, a young woman—or a man—youthful and fond of ornaments, would examine her own facial image in a mirror or in a bowl filled with pure, clear, clean water: she would look at it with clinging, not without clinging. So too, it is by clinging to form that ‘I am’ occurs, not without clinging. It is by clinging to feeling … to perception … to volitional formations … to consciousness that ‘I am’ occurs, not without clinging. [Pali]
’Just as a person who holds in his hand a clear mirror or clean water in a bowl as a mirror and clings to it to see his own face, who sees because of clinging to the mirror, not without clinging to it. [Chinese]
I think upādāya here probably means to ‘draw in’, i.e. one has to ‘draw in’ the mirror towards one’s face in order to see the reflection on it.
The “young woman—or a man—youthful and fond of ornaments” would probably bring the mirror real close to their face, maybe mirroring upa as an intensifier, making it more like ‘pulling in’ the mirror to the face.
So for example, if you don’t want anything, you don’t draw anything in (you don’t draw in any sense pleasures, views et) if you don’t draw in anything, then there’s no content to make up an existence, if there’s no existence, there’s nowhere to get born, if there’s nowhere to get born, no birth, no suffering.
Maybe, food for thought either way 
)