Yesterday I started to practice the song in shorter sections. At first I copy the tab linked in the post on a blank tab paper, then put it on my music stand and start picking. I try to do it with looking at my hands as little as possible.
The most difficult thing so far is to move my 3rd finger on the D string close enough to the frets so that the strings ring out clearly and I don’t lose the time. I started out slow - not super slow but slower than the original recording.
Today I covered bars 11-20 which are almost the same as the first 10 bars but with some variations. I think it’s coming along nicely, so if I’ll be in the mood, I may do the next 8 bars as well today.
The only inconvenience so far is that the fingertips on my fretting hand are getting a rough treatment compared to what I usually do. It feels almost like when I was a complete beginner 
If I won’t have to work too much overtime next week, I think I’ll be able to play the song reasonably well by the end of the week.