Was considering practicing/running for this game eventually; however I only have the Xbox 360 version and no capture card, so I'd be recording from a mobile phone. Were the quality good enough, would I be able to submit a run with mobile footage? I will attempt to capture some footage soon for examples of what my footage would look like in that case, if that helps.

If I remember correctly, someone did Individual Level Runs on a Wii U, and they also didn't have a capture card. I think they used their phone to record the game. If the quality's good enough (let's say 720p) I think the moderation would approve.