I was tossing around the idea in my head that this view of the parable might make sense of Revelation 3:10 (NWT):
Because you [Jesus' disciples] kept the word about my endurance, I will also keep you from the hour of test, which is to come upon the whole inhabited earth, to put a test upon those dwelling on the earth.
It seems to present the idea of some sort of test of the rest of humanity after disciples have "kept the word of [Jesus'] endurance.
In the sheep/goats parable, if Jesus' 'arrival' is placed at/near the beginning of the GT, the sending off into reward/punishment would be at the final part of the GT. The time from the beginning of the GT up to the battle of Armageddon would represent the time during which "all the nations" are divided based on their demeanor towards "the least of these my brothers." With religion under severe stress at that time, it would represent a "test." The parable itself does not hint at how many would choose either way. (Similar to the ten virgin parable in 25:1-12. 5 wise and 5 foolish leaves the amount who would end up either way a mystery.)
The sheep of Matthew 25:37 being called "righteous ones" would be on the basis of Matthew 10:40-42.
By the way, that was an interesting comparison with Paul professing not to know Jesus when Jesus confronted him. It is very much like how the goats respond. Only, in their case, they simply did nothing. Unfortunately, for the goats (in the parable), they were being divided off based on what they did or did not do. (Ebed-Melech would be a similar example of the sheep. Promised survival for helping Jeremiah. His help was counted as an evidence of trust in Jehovah. Compare Jer 38:7-13; 39:15-18)
Another side note is the phrase "the hour of test." (See link for various renderings.) "Hour," as John uses it in his letters and Revelation has a meaning similar to our "time." It is not a reference to length of time. Robertson's Word Pictures points out that John's use of "hour" in Rev 14:6 (as an example) is idiomatic:
"(he hora elthen [literally, "the hour has come"]). Second aorist (prophetic use) active indicative of erchomai. Common idiom in John's Gospel (Joh 2:4; Joh 4:21, Joh 4:23; Joh 5:25, Joh 5:28; Joh 7:30, etc.)."
In other words, "the hour of test" is the same as our English expression, "the time of test." It has no reference to how long (or "brief") the period in question will be. Only that there is a "time " for it. "One hour," on the other hand, would refer to "a brief period." (Rev 17:12; 18:10, 17, 19)
Thanks for your thoughts, Searcher.