So I think the problem I'm running into is that I know too much about DC. To me, anything approaching a full DC universe has too many cosmic and occult forces in play for too long for a difference of a few decades to matter (e.g. the Lantern corps, the New Gods, Nabu, Shazam, homo magi, etc.), and that's not even considering more mundane Methuselahs like Ra's al Ghul or Vandal Savage.
To make this work, I feel like Earth has to be in some sort of enforced neutrality. Let's say that on their final mission in the '50s, the Justice Society is battling some cosmic force that not only threatens Earth but a decent chunk of reality, and end up trapped in a ritual that will drain and dissipate said cosmic horror, but will take decades to complete and is vulnerable to disruption should Earth experience major paranormal upheaval. In the general interests of reality, a number of major players including the Quintessence, Death, Lucifer, and Darkseid all agree that Earth is off-limits until the ritual completes. The gods and powers will still their activity, the occult world will retreat fully into the shadows, and open alien interference will be "discouraged" by the Green Lantern corps.
Of course, the general population of Earth is unaware of any of this. All they know is that their heroes disappeared one day, never to return. By the time the Animorphs are born, decades later, there's some debate as to whether they ever existed in the first place, or if they were just propaganda and marketing. Meanwhile, while the Powers that set Earth's neutrality continue to support it, they've also all moved on to other things as well, or are simply enjoying the short break, so while major incursions are still handled with alacrity and extreme prejudice, more minor affairs slip through the cracks opened by laxity and inattention. Affairs like the odd Skrit Na ship managing to slip the cordon and abscond with some Earth miscellany and a couple teenagers. Of course, the attempted use of the Time Matrix shortly afterwards draws much more attention, but it's resolved quickly and quietly by a rather new power to the region: the Ellimist.
The Ellimist and the Crayak both see potential in Earth. While neither has any current tie to the planet, they are already playing their game with the Andalites and the Yeerks. The existence of powers like the New Gods and others of a similar power level enforces the subtle and hands off nature of the pairs contest beyond even their canonical agreement, and likewise the presence of forces like the Green Lantern corps mean that the Andalites and Yeerks are largely restricted to direct conflict between each other, and much more subtle infiltration efforts towards third parties. In light of this, Crayak sees in Earth a planet of hosts that the Andalites can't openly target, so long as they're taken quietly, while Ellimist sees potential for future agents once the ban is lifted, and if he can play a major role in keeping the planet safe until then, he'll have a better bargaining position to claim said agents.
With this is mind, when Lauren and Elfangor attempt to use to Time Matrix to escape back to Earth, the Ellimist intervenes, and instead transports them directly there while using the Time Matrix himself to remove the time snarl created by its initial contested use. He then delivers the Time Matrix to New Genesis for safekeeping, and continues on with his plans, leaving a replica with Lauren and Elfangor so they are unaware of his interference (yes this means no Elfangor's Secret in this world). A few years later, the Yeerks take advantage of a disruption elsewhere in the sector pulling Green Lantern attention away from Earth for a few days to attempt an initial insertion of a foothold force. When the Andalite force sent to stop them begins struggling, the Ellimist manipulates Elfangor into returning to the fight, preventing said foothold, but leaving Lauren behind without learning of her pregnancy.
Of course, trouble in Sector 2814 is common, so the Yeerks eventually achieve their foothold. Due to their history of imperialism and known conflict with the Yeerks, the Andalites have a poor relationship with the Green Lantern corps, and while they would certainly be willing to point them at the Yeerks, they recognize that without proof they'll probably be shown the door. To this end, the Dome Ship Galaxy Tree is dispatched to surreptitiously visit Earth and acquire proof of Yeerk infiltration, utilizing yet another disturbance elsewhere in the sector. Unfortunately, they run afoul of a heavily stealthed Blade Ship, and Animorphs canon begins.
At this point, events can mostly proceed per canon, with some minor differences. As mentioned above, there's still plenty of potential for non-DC superhero media for inspiration (Marvel actually makes extra sense blowing up big in the 60s, a decade after the JSA vanished, but there's also the pulps, the extensive US-Japanese cross-pollination, the indie comics boom in the late 80s and 90s, etc.), plus now the debatable existence of real heroic precursors. While certain stories can't happen here (such as the aforementioned MM3), for the most part events are fairly local and sufficiently secret (or at least deniable), that the series can generally continue as is.
The one major exception is that Ax, being both and Aristh and a rather inattentive student, is unaware of the Earth's protected status, all he knows is that it's an underdeveloped backwater with no real connection to galactic affairs. To maintain this ignorance, his initial attempts to contact the Andalite homeworld fail, as the Yeerks impose a much stricter communications blackout. #18 can still happen, events move quickly and pretty much everyone who knows the Animorphs are from Earth ends up dead before they can do anything about it, and likewise #38 features a team trying to kill Yeerks and not interested in drawing attention to themselves. I think the penny probably drops only when the Animorphs meet Mertil and Gafinilan, who mention that Earth's quarantined status is both a reason for them to stay, and a reason why they couldn't leave even if they wished. At this point, the Animorphs have an even more clear and direct win condition than calling the Andalite fleet, except that they have no clue how to draw the attention of a Green Lantern. Eventually, in the absence of better options, the Animorphs (mostly) extract their families, and begin to fight more openly. But no help comes.
Unknown to the Animorphs, the ritual completed mere days before, causing the treaty to conclude and the quarantine to lift. While the JSA is recuperating from their ordeal, and higher powers begin reincorporating Earth into their plans, the Animorphs recruit more children and appeal to regional political and military leaders. While Abin Sur travels Sector 2814 to address more minor issues that have accumulated in his decades focused on Earth, the Yeerks begin moving openly and the Animorphs retaliate by bombing the Yeerk Pool. And as Earth's hidden worlds begin paying attention to the mundane side again, it's to the discovery that a group of kids from *****, __ have managed to defeat an alien invasion and placed Earth in a decent negotiating position for what comes next.