With Earth on the brink of destruction, a despairing shuttle pilot leads a team to explore parallel worlds for a new home, but each new Earth they find has already met a cataclysmic fate within a year of own.

"within a year of own"? ?I think there should be a "their" before "own".

Also a "shuttle" pilot? trying to reach other versions of Earth? Seriously? We earthlings aren't up on interstellar flight but wouldn't an interstellar craft be a bit more impressive than a shuttle? How fast are they, because if Earth is on the "brink of destruction", don't have a lot of time to do many interstellar flights, and get the human race to safety especially if all we've got are shuttles.

There is the well worn path of the bigger picture reflecting the internal struggle of the main character. Which is a handy device.

'with earth's death eminent a ship is sent to find a new planet. The only options are all copies of earth on the same path to our horrible fate".

Replace ship with MC and you have my take of your story.

Knightrider:

I like the concept of simulations of earth history.

Have you considered using ye' ol' sci-fi gimmick of parallel space-time dimensions? The simulations are being run in parallel space-time dimensions. In fact, the whole history of the earth as we know about it is one of the simulations being run in parallel space-time, one of numerous galactic virtual machines, all part of a grand experiment in evolution from the same base point event, the same zero-moment when life commenced.

The MC's goal would amount to a desperate quest for a simulation where the experiment leads to a hopeful outcome for life on earth in general, homo sapiens specifically. The ticking clock, of course, is that our simulation is running out of time; we're on the verge of hurling ourselves -- and all life in our simulation -- off the cliff into extinction.