[Kit Webster]"for me to create a time keyframe for this I have to change the time on the layer, and a keyframe is created. Is there a key command that will do this instead? I mean, just say the time of the footage is at 3:30:29"
Usually Option or Alt+Shift plus the shortcut for the property adds a keyframe. However, that doesn't seem to work with the property shortcut for Time Remapping (RR), since it conflicts with the property shortcut for rotation (R).
However, rather than fiddling the values back and forth, you can click the "Add Keyframe" button for the time remapping property to add a keyframe for the current value at the position of the current time indicator. That's the diamond button, in between the two triangle buttons, on the same line of the Timeline panel as the time remapping property, under the the layer visibility, volume, solo, and lock toggles.
See this image:
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