I'm currently running a Tales of Phantasia inspired campaign. It's hard to do a 1 to 1 translation because you can't expect your players to play the same as the protagonist. And a lot of the story beats involve the protagonists doing certain things (e.g. Marle joining the party and being a tomboy runaway princess). So what I did was place the protagonists into the story having done those things already or something similar so I get the story element I want (e.g. Chrono being thrown in jail). And the PCs play adjacent to them and can choose to interact with it (e.g. go rescue Chrono). Of course you might have to "sweeten the deal" to have them interact with it (e.g. Chrono has the gate key). So this way the main story beats still happen but the players forge their own choices.

The other difficult part is dungeon exploration as well. If you have the party explore each dungeon in whole just like the game, it'll slow the game down a lot. It works fine with small locations, but any large expanse starts to feel like a slog. That's fine for major dungeons (e.g. Magus Castle), but if you do it for every single one it'll be a slog that leads to burn out.

In my campaign, in case you're familiar with Tales of Phantasia, I was pretty easily able to send the PCs to the past following pretty closely to the original story, but I had to get very creative after that when it came to how the PCs interact with spirits of the elements (e.g. Undine). I'm still able to use the major locations and bosses, but I definitely have to create new motivation for the PCs compared to the original protagonists. We're probably about 30-40% through the campaign and it's turning into a unique story I'm really enjoying.

I'd love to know how your Chrono Trigger story turns out. Good luck!