I have some personal rules relevant here..
My Personal Rule #1: Re-record if you can!
My Personal Rule #2: Do not stretch anything unless it's absolutely unavoidable. Stretching (here, meaning changing duration independent of frequency) compromises the integrity of the recording in some way, depending on how it's done. Most temporal aligning techniques use frequency-adjusting algorithms. Some don't, which is great, but they only tend to be useable in certain situations (like a clean drum loop). But they do that flawlessly. An example of this is the time-stretch option in FL Studio named, if I remember correctly, "slice map".
How I would do it...
I've never used Logic Pro, or flex time, but when I want to time-sync notes like this, in Cubase (this technique can be done in any DAW), I simply get them lined up at the start, then chop up the clip and line the notes up manually, while trying to respect the original intent of the player - you can use another track with the original recording as a performance reference. It's extremely easy if they're already "Roughly aligned", as you say. Some sequencers allow you to select the sliced recording and compress/expand the timeline just for those clips (i.e. increase/decrease the tempo for the sliced up audio) - this is extremely useful for this situation. The only tricky part will be sustained notes and complex articulations, but you can usually do it easily enough with cross-fading or even just fading in, the next clip. No automated process can do this as well as you can, if you have the will.
Note: This sort of editing does get easier with experience, and you come up with simple little bridging techniques, settings (like auto-fade on split) and even macros to simplify, enhance and make the process more efficient. But even with little editing experience, it should be easy enough for this. It will sound WAY better than digitally stretched and compressed notes.