Here's who is known to have done what, so far. Track titles are based on this playlist so some of them might be a bit awkward.

Kaneda: (source: my correspondence with him)

• Battle Theme I
• Dark Area
• DATS Headquarters Entrance
• Demon Lord Battle
• Distant remembrance
• End Credits
• Hope
• Ice Labyrinth
• Kosaburo's Theme
• Sneyato Forest

Abe: (source: Chimeratio's correspondence with him)

• Boss Battle Theme (reused from Digimon Battle Terminal)
• Comrade Joins
• Doomsday Forest Ruin
• Enemy defeated
• Etemon Battle Theme (+ three short mixes)
• Sea Precipice Jerapilus
• Shopping
• Victory!

Namiki: (source: my correspondence with him)

• Battle Theme III

It's worth noting that Namiki isn't even credited in-game, only on Basiscape's website and his own website. I would assume his track was added so late into development that the credits sequence was already made and then they forgot to add his name in.

Some guesses I have right now, too. Many tracks I'm less sure on, so they're not listed here, and not all of these guesses could be correct either:

Iwata:

• DATS Headquarters
• Mirage Museum
• Rage Cavern

Kamikura:

• Battle Theme II
• Evolution Battle Theme (as well as its short mix, Digisoul Charge!)
• Unknown
• Yuma's Theme

Sakimoto:

• Main Menu
• Opening
• Walter Island/Livilus Island