Tuck leadership essay

Hi, everyone. I'm writing the fifth draft of my Tuck essay, that defines leadership as ïnspiring other to accomplish great things", but still in doubt what will be the best choice to write here about. I have found in my past the following examples, when I stayed out of my cubicle:
1. When I designed and implemented the database that cut down by 60% the amount of time to make the waybills. Earlier they were done manually. Not so much inspiration for other people.
2. When I critically examined the shipping procedures at the warehouse of our main supplier to reduce the number of mistakes that were done there to the 99% complete shipments. Involves some inspiration, but it's more a kind of managerial work to place the write people and write the procedures for them.
3. When our customer changed the specification and tightened the required lead-time I had to find a replacement for one of the products, convince supplier to ship it much-much earlier and finally had to fly to another city to deliver the products in my luggage to meet the final deadline. Here story tells more about taking the lead and convincing people that your case is important.
4. Have been inspiring a girl from another city to prepare for GMAT, giving her support in critical moments and sharing my thoughts for preparation process. Have been pushing her up to the 700-720 that will be enough for second-tier schools she is going to apply to (we'll see if she still wants them after getting 700+ ). An emotional story, but Tuck asks for "great things and great leadership can be accomplished in pursuit of business and societal goals". Is this a societal goal or just good peer support? Anyway, I coach different people to ride the snowboard at my free time (not so many, although) and this is an example of my willingness to share the knowledge I have with people around me and push them beyond their limits.