If the normal methods don't work, you can try doing a full screen capture and cropping it to include only the window+title bar.
Of course, this means you would need to keep the emulator in the same spot every time you launch it or you would need to frequently adjust the crop settings, but it is a way to do what you want if you've already tried doing it properly.
I think you are being asked to provide a video of you performing it, hence the switch capture being mentioned.
While you are doing this, I would pay very careful attention and see if you really are already on the warp star before you technically are supposed to have control (and take advantage of the rewind feature if it makes it easier to tell). It's possible that you just jumped as soon as the intermission screen faded in, in which case the IGT would not be affected.
That is a good question, and a moderator will have to weigh in on this, because I just noticed that the "category rules" and "game rules" are conflicted. The full game leaderboard category rules say "Sound is required.", but the game rules state "Sound is optional, but preferred."