Be aware that if you make a cut in mogrt, then you create N points to edit (if needed later), cause alt+drag creates a new instance of mogrt in a timeline. Plus, if there is any animation, it gets affected and no longer works as expected.
You can control this in Premiere, by adding a slider in AE, which defines animation start time (and ideally, duration how long it should last). Then, link your animation by interpolating from start time.
Things to keep in mind:
1. You need to make mogrt comp time in AE long enough to fit if user defines late start time.
2. You shall not use safety region (well, unless for intro), cause it does not work well with this approach.
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