Je suis bien responsable de tout ça. Il en va de mon devoir moral de vous prêter main-forte.
I assume that this sentence means something along the lines of:
Je me sens obligé par mon devoir moral de vous prêter main-forte.
But I’m not sure how to interpret this construction.
That is correct. The general meaning is that my moral duty obliges me to do something. The simplest sentence would be:
Mon devoir moral est de vous prêter main-forte.
Other constructions are just more formal. Another sentence would be:
Il est de mon devoir de vous prêter main-forte
"Être de" or "en aller de" both express the origin of the obligation, that is my moral duty. However, "il en va de mon devoir moral" suggests that there could be consequences should I fail to help you. Maybe "my moral duty is at stake" would carry the same possible negative consequences, i.e. what kind of person would I be if I do not help you.
Grevisse (Bon Usage, 14e ed. §231 c. 2°) caracterises the expression in a somewhat cryptic way, saying that, along with phrases like il y va de or il en est de, "the prepositional phrase is a complement like that in au sujet de quelque chose".
In any case, it's clear we are not in the same construction as cases such as il suffit de and extracted subject (il n'en était parlé qu'avec le plus grand secret; compare english it was only spoke of most secretively), but how exactly to analyze is left vague. I'm not sure that a parallel with the verbal form s'en aller "leave", where en has pretty much merged with the verbe (you can have an object with de, the same has lead to the word envoler) is appropriate.
I think for the most part these construction are best treated as fixed expressions (TLFi doesn't discuss its history at all), as it is clear the en here is impossible to extract out.
