In Greek the causal preposition 'dia' allows and at times even seems to require a final meaning. (Aristotle had described four causes: material, formal, effective, a n d final cause, which all four respond to the question 'dia ti?' - why?).
Western sciences have - in the wake and philosophical decline after evolution theory depreciated the concept of finality as purely cultural. The end does - in science - not count as a cause (and reason) any more, because nature - according to modernists - can not have purpose.
Meanings (like words) once they are lost are hard to regain. The fourth cause - the final and prospective - has gotten widely disregarded as overly scholastic and biased towards the presuppositions of any given theological (and teleological) concept.
The distinction between causality and finality (almost to an opposition) is a modern one. As the English particle 'for' allows for either meaning (and is short) it is perhaps the best choice to translate the Greek 'dia' in this context. (The change from the retrospective to the prospective dia even adds to the parallel.)
There is indeed a beauty in the wording:
paredothe dia ta paraptomata hemon -
kai egerthe dia ten dikaiosin hemon
given over for the stepping over of us -
raised up for the justification of us
In Mark 2:27 there is a similar use of 'dia':
to sabbaton dia ton anthropon egeneto
kai ouk ho anthropos dia to sabbaton
the Sabbath came to be for the human
and not the human for the Sabbath
Here again it seems quite natural to understand
'dia' as being used in its final sense (of purpose).
If possible, a translation that wants to be faithful to the rhythm and emphasis and weight of the expression, should not render one small particle (here: dia) by two (three) or even four words (like these: because - by cause - of, for the sake of).