I use very much the same process. Writing the song out and then having a copy on the kitchen counter to sing from when I'm working in there. I learn a verse at a time until I have it committed to memory and then go on to the next verse.

I once was told that, whilst we remember the first and last parts of any song more easily, the middle part is always the one that is hardest. I keep that in mind and spend more time memorising the middle verses, particularly the penultimate verse, which is always the one I have most difficulty with.

I think that it helps immensely to know your own weaknesses in the learning process so that you can deliberately target those areas and give more attention.