Here is another stab at it:
Luke: “I started to train her. Leia was quick to learn, but she knew she could better serve the galaxy with diplomacy, as our mother once did. She surrendered her saber to me and said that one day, it would be picked up again by someone who would finish her journey. A thousand generations live in you now. We’ll always be with you, but this is your fight.”
I’d REALLY like leaving the Padme reference if we can. It would be the only time she is referenced in the ST and it would be nice to include as this is the finale to the whole Skywalker Saga.
I tend to agree re: Padme. I think your new line is a good way to get across her skill while making the amount of training even more vague. I’d probably reword the first sentence to “I had begun to train her.”