This reminds me of what happened on the first few weeks of trying out Jamulus. Every musician tries to match the tempo of other musicians. This results in the song gradually slowing down as you described. The next thing we realize is that we are playing songs at 50% speed.

So in the end we designated some instruments to drive the song. Usually its the drums. The person who drives the song must not wait for other instruments and keep their own tempo, and everyone else try to time their instruments to be in-sync with the drums. It works quite well for us.