I would learn the first one to where I was comfortable with the song and could play through with very little distraction of thinking "what's next".
Then learn the next one the same way.
Then go back to the first and improve it, move on to the second and improve it, then add the third.
Pretty soon you'll find yourself just playing through the first one to get to the next and next .. so you can focus on a new one again (psychological side of it). Plus the discipline of going back reinforces muscle memory.
Not long after you get to knowing 3 or 4 you'll know 10 .. improvement comes with practice on this task just like others; you'll start to get faster at it the more you do it.
Don't just try to learn one, then the next, then the next, remember to go back go back and re-remember the ones you did previously. It'll only take a few minutes and keeps them fresh in the mind ..I think of it like a computer uses cache <grin>; it's worth storing special if you are going to need it often. This exercise helps your mind keep it in the 'recently needed' area and fresher in memory for faster recall.