JFZ, I stand to be corrected, but from what I understand, the ALARP principle in the way you describe it in relation to TWA800 is not right. Large civil aircraft are certified against the numerical objectives as stated in FAR25/CS25. The 1x10e-7 hull loss target, which in turn leads to the 1x10e-9 target for critical systems. This is stated in requirement 25.1309 and the Acceptable Means of Compliance (AMC) expands this, see CS AMC25.1309. You can download CS25 from EASA for free. ALARP is not mentioned in the context of certifying an aircraft of this type, you achieve the target or you don't get certification. The ALARP principle is really encapsulated in the target itself, this is based on the historical hull loss rate with a precuationary factor built in.
As I am sure you are aware, ALARP is a principle based in UK case law from 1947, and results from a case involving the coal mining industry. There are variations on this theme, eg AFARP.
S_H