That's right. I think a tale in which the forces of good had already "won" would inevitably have a tone that was unsatisfactory in its variance from that of The Hobbit and LOTR.
Had Tolkien really wanted to write another "quest" novel, he might have been better persuaded to transmit one of the stories that would later appear in the Silmarillion in that style.
I think the only way to do it (and I'm not saying it would be satisfactory) would be to bring in the Blue Wizards. Tolkien himself said he suspected that they were founders or beginners of secret cults and 'magic' traditions that lasted beyond the fall of Sauron, so he may have been thinking along those lines also when he started his Fourth Age story "A New Shadow". Maybe not though because he also said something to the effect that there was no evil beyond the evil of men (I think there were other reasons also).
There were remnants of Elves, Dwarves, Ents, etc. left in the Fourth Age, but clearly they would never reach to power of their respective races during the Third Age. In fact, if you think about it, Tolkien's writings were all about the fading of power from the very beginning of his writings.
Yavanna created the two trees of Valinor, Laurelin and Telperion in the early days after the creation of Arda (the world) and could never duplicate that feat again as much of her power went into the creation. Nienna, one of the 8 Aratar (the great of the Valar) was able to bring forth the last fruit and flower of the trees which became the sun and the moon.
The end of the First Age and the downfall of Morgoth saw the mightiest host ever assembled against him. The end of the Second Age and the first defeat of Sauron (and the taking of the ring from him) saw the Last Alliance of Elves and Men. Yet Elrond himself (who saw both hosts) said the Last Alliance was not so mighty as the host that overthrew Morgoth. Clearly the Army assembled against Sauron at the end of the Third Age had no hope of defeating even a diminished Sauron (being without the ring). Anything in the Fourth Age would probably have continued, but I can guess that the army of men may have grown (along the lines, but not so dramatically, as the hosts of Numenor).
In any case, this is all conjecture (except for the fading of power of the those bound directly to the fate of Arda...i.e. Valar, Maiar, Elves, etc. and "not" Men) and the work was abandoned.