If your use of the tremulant extends into any of these "inappropriate' situations, it may not seem easy to change. The music may sound more dry and less interesting to you without the tremulant to which you may have become accustomed.
Most organs have some stops or combinations that are very beautiful in and of themselves. We sometimes mask these simple beautiful sounds by using the tremulant or by stacking together too many stops.
Spend some practice time listening carefully to each stop of the organ. Identify the stops that are most beautiful. Play some of your favorite organ music or hymns on each of these stops or combinations without the tremulant. You may discover characteristics of tone that you have never allowed yourself to hear.
Excellent playing on beautiful stops without the tremulant is simply uplifting.