Do Jehovah's Witnesses believe only they will be saved after their organization came into existence?

The Watchtower Bible and Tract Society was founded in 1886 by Charles Russell. He and his followers were known as Bible Students and “Russellites” until 1931 when the second President, Joseph Rutherford, renamed the organisation as “Jehovah’s Witnesses.” Jehovah’s Witnesses believe that true religion became corrupted after the first century, and especially when the Catholic Church came to power. Between then and 1886 they claim there have only been a very small number of true Christians. Then Jesus chose them as his earthly organisation in 1919:

1 April 2007 Watchtower, p.22: “‘On arriving’ to inspect the ‘slave’ in 1918, Christ found a spirit-anointed remnant of faithful disciples who since 1879 had been using this journal [the Watchtower] and other Bible-based publications to provide spiritual ‘food at the proper time.’ He acknowledged them as his collective instrument, or ‘slave,’ and in 1919 entrusted them with the management of all his earthly belongings.”

February 2017 Study Watchtower article: Who Is Leading God’s People Today? “8. In the late 19th century, Charles Taze Russell and some of his associates endeavored to re-establish true Christian worship... 10. In 1919, three years after Brother Russell’s death, Jesus appointed “the faithful and discreet slave.” For what purpose? To give his domestics “food at the proper time.” (Matt. 24:45)”

Below are quotations from their own publications on who will survive Armageddon:

15 February 1983 Watchtower, pp 12-13, article You Can Live Forever in Paradise on Earth​—But How? subheading Four Requirements: “Jehovah is using only one organization today to accomplish his will. To receive everlasting life in the earthly Paradise we must identify that organization and serve God as part of it.”

Watchtower December 15, 1975 p 753: “Only Christian witnesses of Jehovah who successfully pass this test will survive and come forth like fire-refined gold for God’s use in his precious new order.”

Watchtower September 1, 1989 p 19: "Only Jehovah's Witnesses, those of the anointed remnant and the "great crowd," as a united organization under the protection of the Supreme Organizer, have any Scriptural hope of surviving the impending end of this doomed system dominated by Satan the Devil."

Watchtower September 15, 1993 p 22: “But if we were to draw away from Jehovah’s organization, there would be no place else to go for salvation and true joy.”

Watchtower May 15, 2006: "During the final period of the ancient world that perished in the Flood, Noah was a faithful preacher of righteousness. (2 Peter 2:5) In these last days of the present system of things, Jehovah's people are making known God's righteous standards and are declaring good news about the possibility of surviving into the new world. (2 Peter 3:9-13) Just as Noah and his God-fearing family were preserved in the ark, survival of individuals today depends on their faith and their loyal association with the earthly part of Jehovah's universal organization."

Watchtower December 15, 2007: "But Jehovah's servants already belong to the only organization that will survive the end of this wicked system of things."

March 2016 Watchtower article Jehovah Guides His People in the Way of Life: “Indeed, to keep receiving God’s blessing, we need to pay attention to all the directions provided through the Christian congregation. Having an obedient spirit now will help us to follow directions during the “great tribulation,” which will eliminate Satan’s entire evil system. Thereafter, we will need new directions for new world living on an earth totally free of any satanic influence.”

November 2016 Study Watchtower article They Broke Free From False Religion: “In 1919, a “faithful and discreet slave” was appointed to provide spiritual food to the household of faith. (Matt. 24:45) God’s people were now free of the influence of Babylon the Great.”

Jehovah’s Witnesses also believe the Antichrist is made up of Trinitarian churches "promoting the use of Bible translations that omit God's personal name, Jehovah, from the text." June 2015 Watchtower article Who is the Antichrist? http://www.jw.org/en/publications/magazines/wp20150601/who-is-the-antichrist/

Today, Jehovah’s Witnesses believe only they will survive Armageddon. They view every Christian denomination (whether Catholic or Protestant) as part of Babylon the Great, the harlot of Revelation, soon to be destroyed. However, they never say that to non-Witnesses when they go from house to house. They are careful to promote the idea of living forever on a paradise earth after Armageddon.

I am unaware of any official statements that indicate they do NOT dogmatically believe that they are the only channel of God's truth and direction today, or that today, one does not have to be a Jehovah’s Witness to be saved. Of course, such statements may exist and if they do, I would be pleased to read them.