I'm going to divide this into sections, because there's a lot to cover.
1. Visual Aspect
I would probably start by sketching out the first few areas of the game using a perspective closer to the 3/4 top angle used by most SNES-era RPGs (Fort Dragonia dreamscape, Arni, Lizard Rock, and Opassa should be enough to start with). A lot of the locations in Cross were drawn at a flatter angle that would be difficult to work with as tilemaps with constant-sized sprites (the upper area of Termina outside Zappa's shop is one of the worst, but there are others).
For the tiles themselves, you may be able to steal a few from Trigger--the Forest Maze from Prehistory has appropriate sandy soil and palm-like trees--but a lot more are going to have to be drawn from scratch. And then they need to be fitted together into maps.
Then you need some sprites. If you cheat and hard-code Radius as the third character in the dream sequence, you can get away with three full PC spritesheets (Serge, Kid, Radius) plus some Arni villagers (walking animations at most, set must include Leena) and a half-dozen monsters for the first stage of the game (up to Arni (Another)). The PC spritesheets need the usual basic animations (walk, run, attack, defend, cast, die, possibly climb and idle).
2. Audio Aspect
All the music would have to be downgraded to fit the SNES's limited four-instrument system. Not sure how many channels there are in the original, but there's going to be something somewhere that doesn't fit, and the instruments themselves are going to sound more synthesized.
Also, you're going to lose the vocal from the ending theme no matter what you do. The SNES was never known for being good at reproducing intelligible speech.
3. Programming Aspect
Where do I even begin? Cross's combat system doesn't entirely match up with any other JRPG ever, as far as I know. Even if you started with a Trigger ROM as a base (probably not a good idea), you'd have to reprogram the combat and Elements systems largely from scratch. In SNES assembler. That's likely going to be a major time sink.
The menu, with its quirky rotating pointer, is another thing peculiar to Cross. I think there was someone who produced a working version of that, some years back, so if you're serious about this, you might consider searching the boards on romhacking.net and see if you could find them. The Element grid support is going to need to be written almost from scratch (you might be able to reuse some stuff from the equipment system).
And you're going to run into various size and complexity limitations imposed by the SNES hardware. Mauron's already mentioned one. Plus, even with the video cutscenes reduced to sprite animations and a lot of the Element and enemy special attack animations simplified, I suspect you may also run up against the "how much can you fit in a cartridge" limitation. You may have to pare away everything that doesn't figure into the main plot, and then judiciously cram as many of the cut bits back in as you can find room for.
Alternatively, you could move to another engine and just mimic the SNES graphic style, although I'm not sure what the point would be, then.
In short, it's a really big project, and I can only wish you luck. If you want to know what you, personally, should try to learn to have the best chance of pulling this off, I'd look into the programming side.