Is it possible your worship team is attempting to fill too much musical space?
Think of an incredible painting, photo, or sculpture. There are incredible details that go into each piece of art, but most brilliant pieces have a single focal point. That is, your attention is drawn to one piece of the art. The other details exist primarily to support the main focal point.
Have you ever found your worship team playing more and more just to try to fill space? Chances are you have. More strumming on the guitar, more incidentals on the piano, harmonies harmonies harmonies, etc.
Some songs can successfully involve a lot of intricate rhythms and parts with ease. But the majority of worship songs benefit from a "less is more" mentality.
That means, instead of trying to jam your amazing new strumming pattern into every song on your setlist, be intentional about what each song calls for. Less rhythm, more melody, less dynamics, more gusto, etc.
Try it at rehearsal this week. Take one song you typically "over-play", and try to do significantly less with it than you would normally do. Draw attention to a single chord or harmony line. Let the music speak for itself!
A beautiful way to catalyze the "cure for overplaying" is to use worship pads. Turn on a pad MP3, and it will give you a beautiful musical bed so you don't have to fill the musical space. You can be choosy and intentional with every musical decision you make. Playing fewer notes allows you to be less of a "hole-filler" and more of an artist.
I promise you, less is more. Take it from a guy who tried to sneak every musical lick he knew into every performance situation possible. Strip it down, make intentional choices, and draw attention to that singular focus.