Where is the leaderboard for the time trials in this game if that is even ran at all? I've done a couple runs and got around a 2:22 in Terra Island 1

Time trial leaderboards are currently well established on other sites. Here are the relevant links:

English CNK GBA: https://www.cyberscore.me.uk/group/1813/10995
Japanese CNK GBA (TT times): http://crashhouse.curahome.net/crashtime/?game=nc_gba_timetrial
Japanese CNK GBA (Trophy times): http://crashhouse.curahome.net/crashtime/?game=nc_gba_timetrophy

Here too:
http://retroachievements.org/game/5127

Maybe the mod could make a time trial section on this site too?

No reason to make a time trial section on this site if there are plenty out there.

Is it video evidence on the japanese site?

video evidence is optional from what I can find on that site

Would like to see cus there are some very good times there, but it's in japanese so don't know if I'll find it