If this was to be fully rewritten, I feel that Taylor having a little more restraint (like how she held back from harming her bullies in canon, if only barely, for about 4 months after the locker), yet not outright letting them walk over her would be better.
Kind of like how it went in this story, only instead of how Taylor:
Killed Gladly and proceed to run down the street killing animals like a maniac before killing Lung, only to get found out the next day.
Instead, I think having her start with the more esoteric uses like how Takatou Yogiri did later on, such as killing her momentum, killing bullets, or even killing her limits to allow herself to grow stronger to Brute levels, possibly killing bugs or not doing so before not using that, and perhaps (depending on if she knew she could kill people at the time or not) kill Lung when she goes out in fear, either knowingly or not.
After that, whether she decides to use it again, hide the power in fear, or hold it as a last-resort, a trump card to be used in the most dire situations - it really depends on how you'd have her personality change from this.
Perhaps she'd kill one or multiple S-class threats, possibly including an Endbringer pre-emptively or during one of their attacks for the latter case from a distance, or she shows up in person to do the act - it depends on whether you'd like her to hide her power or not.