But I recall it implied that all the 144k could die off and the Org would be run by the "given ones" until the Big A. Did you get this too?
That's the impression that has been given, yes, though they don't come out and say that explicitly.
Here's the exact wording in the 1992 article:
In ancient times, priests and Levites continued to serve among the Jews. (John 1:19) Today, however, the remnant of spiritual Israel on earth must go on decreasing. (Contrast John 3:30.) Finally, after the demise of Babylon the Great, all 144,000 ‘sealed ones’ will be in heaven for the marriage of the Lamb. (Revelation 7:1-3; 19:1-8) But now the other sheep must go on increasing. The fact that some of them, comparable to the Nethinim and the sons of the servants of Solomon, are now being assigned weighty responsibilities under the oversight of the anointed remnant does not cause them to be presumptuous or feel self-important. (Romans 12:3) This gives us confidence that as God’s people “come out of the great tribulation,” there will be experienced men—“princes”—prepared to take the lead among the other sheep.—Revelation 7:14; Isaiah 32:1; compare Acts 6:2-7.
Another article was in 1995 (w95 7/1 pp. 21,22):
7 In 537 B.C.E., when Israel returned from exile in Babylon, they set about organizing service on the temple site. However, the Levites who returned were not very numerous. Hence, the Nethinim—circumcised alien residents who previously were assistants of the Levites—were given increased privileges in temple service. They were not, however, equals of the anointed Aaronic priests.—Ezra 7:24; 8:15-20; Nehemiah 3:22-26.
8 Anointed Christians today have followed this pattern. As “the time of the end” has progressed, the remaining ones of the anointed have become fewer and fewer in the “land” of God’s people. (Daniel 12:9; Revelation 12:17) In view of this, the great crowd now accomplish most of the work of rendering “sacred service.” (Revelation 7:15) Following the lead of their anointed brothers, they “offer to God a sacrifice of praise, that is, the fruit of lips which make public declaration to his name.” They “do not forget the doing of good and the sharing of things with others,” knowing that “with such sacrifices God is well pleased.”—Hebrews 13:15, 16.
9 Moreover, with the great crowd increasing by the hundreds of thousands each year, there is an ever-growing need for oversight. At one time this was handled exclusively by anointed Christians. Now, oversight of most congregations, as well as circuits, districts, and branches, has of necessity been entrusted to the other sheep. In 1992 a few of these were given the privilege of attending meetings of committees of the Governing Body and serving as nonvoting helpers. Still, the other sheep remain loyal to their anointed fellow Christians and feel privileged to support them as Jehovah’s faithful and discreet slave.—Matthew 25:34-40.
I suggest you also look at w97 5/15 pp. 15-19 as it has a discussion regarding the other sheep and its responsibilities. A search for "Nethinim" or "given ones" in the WT Library CD might be helpful.