I've been wanting to make an "NAR but stupider" for a while. My plan was basically golden rule + some special cases for common scenarios it doesn't cover, ignore everything more complex.
For an action resolution system that covers everything, there's
RAR. I tried it on your scenarios:
> A blocks B and kills C, B protects C
C was killed, but B protected them, but A blocked the protection. No circularity, kill goes through. (RAR produces the same result as NAR and DAR in all golden-rule-only scenarios.)
> A blocks B and kills C, B jailkeeps A.
C was killed, but B blocked the killer, but A blocked the block. We can't go further at this point (you can't apply the same action twice in a chain in RAR), so in RAR the kill goes through. This differs from DAR. NAR as originally defined is silent on the issue. There's also an official ruling for Normal games (which otherwise use NAR), which has a Roleblock always take precedence over a Jailkeep in action loops, so in a Normal game the kill wouldn't go through (although it wouldn't if A were a scum jailkeeper and B were a town roleblocker).
I originally had the Normal NAR result backwards; edited
> A redirects B to C. B blocks A. C investigates D.
C investigated D, but A redirected a block onto them, but the redirection was itself blocked. As usual in RAR, we have to stop here; the redirection was already involved in the chain and thus it can't also be used to save itself from being blocked. The investigation goes through. This is different from DAR.
> Bonus round: A redirects B to C. B blocks A. D watches C.
The only argument in favour for D getting a result is that A redirected B to C; but B blocked A, and the redirection has already become part of the chain so it can't be used to stop the block too. D sees nothing.
I'm not claiming that RAR's, Normal NAR's, or DAR's results are necessarily better (although I prefer both RAR and DAR over NAR because the tiebreak is less sensitive to the details of the roles). RAR pretty much just exists for a "system that resolves everything in a fair way", rather than necessarily to always produce the most intuitive or most balanced result. I was mostly just curious to see what would happen in these cases.