I think about time and space too.
Like, how can she best avert the entire episode? She should likely appear to herself before her past self even enters the shuttle, to tell her about orbital objects and stupid assumptions. She can then have the aid of her past self in using the station to transmit the barrier warning to the Kelvin fleet.
Early arrival is the best bet for averting the mission entirely, possibly saving her past-self from getting kidnapped. Worst case, the is a future clone of herself along with the contemporary version. That presupposes no reverse causality, as in killing your father in the past before you are born does not make you disappear, which fits with a more stable supposedly self correcting temporal cosmology.
More fitting with other Trek stories, she might appear in the shuttle just before the experiment. Maybe she knocks her past self out with a pistol whipping, then remotely hacks the station to relay the warning. Then to tie things up, she time travels pastward in the time shuttle to get off in the 21st century to live a quiet self imposed exile. She sets the time shuttle controls to send her past self, who is still in the shuttle, back to the future safely with a warning, or some sort of Scotty-esque sabotage of the temporal circuit.
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