As a matter of fact, I've never even played Chrono Trigger
But yeah. I prefer to make it a mid to low priority because I don't want the game to be majorly associated toward time travel. This is why I would rather keep it as an optional part of the game. But I would add parts of the storyline based on the past.
My idea for the past is that there is a storyline behind it which is optional. What I said in my last post was just a "hinted" idea.

Not just for the pure whim and woe of an ironic item in the past and present. My idea was about the civil war and the discovery and struggle of a resistance. This is purely optional, but if complete, you uncover something say, valuable, and a worthwhile piece of information. Further exploration in the past allows you to access more areas which you could normally access in the present.
My idea of a past is several years ago, 30 years ago, was my idea, and time travel is rather more limited, where you must walk up to, say a "Maw Rift" which sucks you in by accident. You are put into the past of that area, and you can only access the present by re-approaching that Maw Rift. So for now, only that area alone you have access to.
To access other areas you need to explore more areas by walking to them manually forsay. And within those areas you need to locate a Maw Rift in those specific areas. Activating rifts in the past allows them to flow in the present, allowing you to access the past area of that specific location once activated from the past.
Areas such as towns and cities for example, play a major role in the storyline of the past. As you find out there is about to be a war between civilization and monster. I plan on it being set into the Mideval Era, so there are swords and shields ect. You have the option to join forces of a specific nation. (Which I would call a campaign battle for example.)
I also plan on making classes unlocked exclusively for accessing the past. Locating a city say, is a rough journey, but worth it, allowing you to trigger quests in that city. Some of those quests require you to travel outside the city agian, but you are able to teleport to areas you've activated by speaking to Allied Reunion Sappers at outposts in specific areas. The outposts serve as strongholds while monsters--or beasts, rather--try to take over them. Battles take place there and you try and fend them off, this is how you do your part as an Allied Campaign Soldier for example.
That's just an idea of what I'm going to try and achieve. I think the idea can succeed well with the right tracks set in motion.