This was the question that long ago brought me to kwakerskripturestudy.
A search on "everlasting gospel" led directly to here, and to a passage in Revelation:
"Then I saw another angel flying in midheaven, with an eternal gospel to proclaim to those who dwell on Earth, to every nation and tribe and tongue and people; and he said with a loud voice: "Fear God and give Him glory, for the hour of his judgment has come. Worship Him who made Heaven and Earth, the sea and the fountains of water."
Is that message "Quakerism"?
For early Friends, they would certainly have agreed that spreading "the Gospel" was precisely what they were doing. And that formulation of it, I think, would have been approved.
For modern Friends, it might be hard to find agreement.
That is one reason why early Friends made many converts, while modern Friends do not. Not only did they have a clear message; but it was one which many of their contemporaries were prone to credit.
It is not that they had a preferred form of words for saying it. But they knew The Gospel; hence they could put it into appropriate words for anyone capable of believing it. Why can't we say, as they would, that 'Quakerism' is the gospel, and The Gospel is Quakerism?
How were they different from other preachers of their time? They had a very spiritualized understanding of what the Bible meant, a very 'inward' understanding of where God dwells and how He may be known. They could point each person to the One alive in them, the One who could show them their faults-- but only so these could be forgiven and they might be led away from all such afflictions.
And they had a very concrete understanding, as well. Because, when you know that the Spirit is real, that changes everything! Their faith was strong enough to make manifestations of the Spirit, in their concrete lives, phenomena they could expect and rely on.
So, do we know what 'the Gospel' is, and how to convey it? This message that was explicit for early Friends, implicit (and hardly credited) for modern ones...? A "gospel" is "good news" announcing the advent of a new world ruler. In the case of our example from Revelation, I can paraphrase: The true ruler of this world, this very world, this woefully fallen world, the One who is our true Judge, is the Being of infinite love, wisdom, goodness, and mercy.
"Oh, the first days are the hardest days; don't you worry anymore!" (Grateful Dead)
& you say, "Yes, but..."? Okay, what can you say about this? & what does it have to do with being "Quaker"?