The best way to go about perfecting your hymn playing skills is to find a hymnal you could use at home for your own practice every day. Depending on your level of proficiency on the organ you might want to make things easier or more difficult for yourself.
What I mean is that if you are good in sight-reading four-part harmony and chords, then you could play four parts right away. Do this in a slow tempo for several months in a row and you will be quite competent in playing the hymns in four parts fluently.
However, for people who have weak sight-reading skills, I recommend practicing in separate voices first. For example, when you open your hymnal, play just the soprano part of that hymn. Then take another hymn and also play the soprano part. Do this for a number of hymns. After you sight-read the soprano line of about 100 hymns, you can go back to the beginning and start practicing the alto line.
Later take the tenor line and the bass line in the same manner. When this becomes easy, start playing two voices at a time and later three voices. There are many combinations of two-part playing and three-part playing so make sure you cover all of them in your hymn-playing. After the last combination you can go back and start practicing these hymns while playing the entire four-part texture.
This way you can become quite competent in hymn playing regardless of your current technical limitation. This type of systematic approach to hymn-playing is very simple yet very powerful. However, it is not easy to follow through because it takes many days of consistent and regular practice.
If you apply my tips and aim for at least three correct repetitions in a row of each particular hymn, you will discover some tremendous changes in your sight-reading of the hymns and you will be able to play them with fluency and ease.