The video below specifically works on “I Surrender All,” but the style is appropriate for invitational hymns, in general. The main point to remember when playing for an invitation or time of prayer is to play much more softly than you do for congregational music. You are there to provide more of an atmosphere and a spirit of prayerful meditation than anything else. This is not the time to practice your arpeggios and Southern gospel frills or jazz chords. Just keep it simple. 🙂 Even playing just the four notes from the hymnal with a few connecting fill-ins is sufficient. I usually keep the soft pedal pressed the entire time I play for invitations, unless the congregation is asked to sing a verse.
You can also just play two or three notes in your right hand (melody, then add an alto or tenor harmony) and keep a soft rolling pattern in your left hand, as seen below.