This very dense article by one Kevin Slack is found here. There are many good things in this article, most of which I've already seen; but it did manage to deliver something I hadn't noticed before and which I haven't seen either from most contemporary scholars of Ben Franklin and religion.
Apparently Franklin was involved in a liturgy project with one David Williams. From the article:
As a member of the Thirteen Club, Franklin helped David Williams construct A Liturgy on the Universal Principles of Religion and Morality in 1773–1774.258 Franklin told Williams that he “never passed a Church, during Public Service, without regretting that he could not join it honestly and cordially,” and he wished to revive a “rational form of devotion,” like that of Shaftesbury's deism, for freethinkers.259 Church attendance had declined, and there was no alternative to the liturgy of the Book of Common Prayer or Dissenter enthusiasm.260 He “thought it a reproach to Philosophy that it had not a Liturgy and that it skulked from the public Profession of its Principles,” and he lamented the loss of “that pleasure, which all virtuous minds have in a public acknowledgement of their duties.”261 A liturgy was needed to preach the general principles of a common creed: “All disputed opinions should be excluded public-worship; and that all honest, pious men, Calvinists, Arians, Socinians, Jews, Turks, and Infidels, might and ought to worship God together in spirit and in truth.”262 Thus the liturgy invited the many of all faiths to join in a common creed constructed for a select “Party of Virtue.”263
The bold face is mine and it's an exact quotation from their project.
One reason why this piece of evidence may have flown under the radar of many scholars is that the evidence of Franklin's involvement in the project comes mainly from David Williams and not Franklin. However, I have found one letter of Franklin's to Williams and two letters (one and two) from Williams to Franklin.
The letters discuss their project. But in any event what was quoted above in bold reflects as far as I can tell Ben Franklin's adult opinions on both public (political) and private (personal) theology. And it's fairly close to Jefferson's and J. Adams' and thus explains the generic, "non-disputed" God language of the Declaration of Independence.