What is the origin of the word "efforting"?

Solution 1:

Early 'efforted'

Wiktionary's dating of the Thomas Fuller example (mentioned in user240918's answer) refers to a later edition of Fuller's book. An edition of Anglorum Speculum did indeed appear in 1684—but an earlier edition of the text, titled The History of the Worthies of England Who for Parts and Learning Have Been Eminent in the Several Counties and containing essentially the same wording that appears in the 1684 edition, was published in 1662, one year after Fuller's death. The instance of efforted in the 1662 edition is as follows:

Two Captains being at dinner, one of them fell into a large relation of his own atchivements, concluding his discourse with this question to his fellow, And pray sir (said he) what service have you done? to whom he [John Smith] answered, Other men can tell that. And surely such reports from strangers carry with them the greater reputation. However, moderate men must allow Captain Smith to have been very instrumentall, in setling the plantation in Virginia, whereof he was Governour, as also Admiral of New-England.

He led his old age in London, where his having a Princes mind imprison'd in a poor mans purse, rendred him to the contempt of such who were not ingenuous. Yet he efforted his spirits with the remembrance and relation of what formerly he had been, and what he had done. He was buried in Sepulchres-Church-Quire, on the Southside thereof, having a ranting Epitaph inscribed in a table over him, too long to transcribe. Onely we will insert the first, and last verses, the rather because the one may fit Alexanders life for his valour, the other his death for his religion; ...

The meaning of efforted in this excerpt does seem to be "stimulated" or perhaps "sought to raise."

Early 'efforting'

The earliest instance of efforting that I have been able to find is from a strange book that offers uncertain insight into how the author intended the word to be understood. From Wlliam Freke, Lingua Tersancta: Or, A most Sure and Compleat Allegorick Dictionary to the Holy Language of the Spirit : Carefully and Faithfully expounding and illustrating all the several Words or Divine Symbols in Dream, Vision, and Apparition, &c. (1703):

Left side step to, that is, err in your Proceeds, at least for the present. ... Persons seen there, Courses to be deem'd efforting to your worst, as &c. | to your right è con. as is the Person and Character.

Freke's book undertakes to identify the symbolic meaning of various actions and images encountered in dreams, which he does at great length and in considerable detail. Here, efforting seems to mean, as it does in the modern sense of the word, "to make an effort."

The next earliest source to use efforting is Augustus Cove, The Tocsin Sounded a Second Time! or, The Bull Taken by the Horns!!! number 2 (1813), which uses it three times, again in the modern sense:

in this situation I began to feel considerable alarm, that some remarkable personal harm was intended me, and that his [John Weston, alias the Butcher's] object in wishing to have the window shut, was to conceal the deed;---for abstracted from that, no motive could be assigned;---this reflection coupled with the angry and menacing appearance of the man, occasioned me to call out MURDER many times, and after various strugglings, I got upon my feet and endeavoured to reach the window, which he as resolutely was efforting to prevent, and in order to do so he called to Sharrat to come and assist him; ...

...

To 5 years mis-gain, at the rate of 300l. per annum, through the Company's default as stated in pages 38, 39, for I had the business, which was done Gratis, or only my proportion of it. it had probably resulted in a profit of 8 or 900 a year, instead of which, though variously efforting, by the unaccountable laxity of the Company to my interest and their own, I got nothing at all, that 300l. is reasonable, even the very rise in rent, intended by the Company, is a Proof.

...

But the latter part conveyed an idea not so true, certainly I depended upon Charles Harvey seeing me compensated---but I did not so rely upon him, as upon the obvious legal demand I had upon the Company, whether C. Harvey was a true man or the contrary ; to Nonsuit a man and subject him to expence, as may so cripple his powers---as to disable him from efforting again---that had received so great an injury, ought not to be done, but upon very obvious and clear reasons; were I to make a blinder, and commence a suit against John Doe instead of his brother in la Richard Roe; I should understand the Nonsuit---and submit quietly---but this I cannot comprehend at all!

On the one hand, I sympathize with Mr. Cove for having endured the Bleak House treatment at King's Bench; but on the other, anyone capable of assembling 185 pages of full-bore denunciation—as volume 2 of a literary campaign that he promises is "TO BE CONTINUED" in future numbers—shows signs of being perhaps a bit intemperate and litigious himself. Still, his attachment to efforting can only be admired.

Conclusion

In my research, I didn't find any instances of efforting used in the obsolete transitive sense that Wiktionary attributes to effort as a verb; the instance of efforted that Wiktionary cites is legitimate and interesting, but I didn't find any other instances in which efforted clearly carried the old sense of the word.

Instances of efforting in its modern sense of "striving or making an effort" go back at least as far as 1703. The Ngram graph for efforting over the period 1600–2008 indicates that the word has never been widely used in published English. It's possible that word has been recoined or reinvented on several occasions, with the same predictable meaning of "making an effort" each time, rather than having enjoyed continuous use since it appeared at the dawn of the 1700s.

Solution 2:

Effort as verb appears to be either uncommon or obsolete:

1) (uncommon, intransitive) To make an effort.

2) (obsolete, transitive) To stimulate.

• 1684, Thomas Fuller, ‎G. S., Anglorum Speculum: Or The Worthies of England, in Church and State‎[1]: When old, he lived in London where, being High-minded and Poor, he was exposed to the contempt of disingenuous persons. Yet he efforted his Spirits with a Commemoration of the Days of Old.

(Wiktionary)