Page 452 of the manual talks about Autopunch recording - which I think will help you out:
"...Logic Pro will begin recording approximately one bar before the punch-in locator. This allows the start point of the region to be adjusted later, enabling you to hear the lead-in, if desired.
You can also recover the beginning of the recording if the performer slightly anticipates the autopunch area. Any such adjustments to the lead-in portion of the region do not
change the position of the recording, relative to the time axis of the project...
Combining Cycle and Autopunch Recording
If you want to improve a difficult part of a certain passage, you can use a combination of the Cycle and Autopunch functions. Cycle mode recording allows you to practice as
many times as you like before performing the final take. On each cycle pass, only events or audio that falls within the area defined by the autopunch locators is recorded. This
allows you to make use of the preceding song section to get into the groove."
This looks like it should help with the drop-ins. I'm not sure that you will need to use fades.
Also, there is nothing wrong with playing the section through a few times -
a) Logic will let you build a composite of the best parts of multiple takes
b) if you can get it right in one take then your problems are solved.
I strongly suggest you watch the 101 course, and take a look at the Audio punch recording section of the Logic manual.
Just going back to your first post, I'm not sure if you would beat map the final result - do you mean use flex time? To tighten up your strum to fit the beat?
Let us know how you get on!