As you know, the parts of the hymn harmonizations in our hymnals are distributed so that the hymn melody is in the soprano, then comes the alto as the second highest voice, then the tenor and the bass.
What would happen if you could play an arrangement of your hymn with the tune in the tenor? The benefit of this method is that soprano and the tenor switch places. The result - completely different melody is in the top voice (usually very smooth and singable). It's not too difficult to do - you simply play the hymn as written but with the tenor one octave higher and the soprano one octave lower. Interestingly, the chord position is also inverted - open position in the original becomes closed here and vice versa.
Another possibility would be to place the hymn tune in the alto. In order to accomodate the voice ranges, sometimes the hymn should be transposed a perfect 4th or a 5th downward. Keeping the bass and the harmony the same, you will have to create the new tenor and soprano parts.
The hymn tune can also be played in the bass. This arrangement often produces very different harmonies from the original. When working on harmonizing the bass, aim for the smooth soprano part and contrary motion with the bass.
When you play your hymn on the organ in any of the above ways, it's best if you could choose a solo registration for the voice with the hymn tune - softer or louder reed, combination of flutes and mutations, a cornet (if the range permits).
Try one of these arrangements in preparation for your service playing with the familiar hymn next week. Not only you will be pleasantly surprised with the result, but your congregation will be delighted, too.
You can play 4 different stanzas of the same hymn in 4 ways. However, if you haven't done these experiments before, remember that it takes more time than it seems to be fluent with placing the hymn tune in any voice so start small at first.