I you don't mind sacrificing a reed or two, you can hook up the suction end of a vacuum (perhaps a Shop Vac type) cleaner hose to the exhaust end of the call and turn the vacuum on. It might burn out the motor of the vacuum if done too long without a pause, but it will speed up the break in process. The reed may develop bubbles on the edges of the reed where they come into contact with the tone board, so that's why the reed, or two, should be considered sacrificial. When I tried it, I used a Shop Vac and applied the suction in intervals of about 15 seconds before a break, then repeating for additional periods. I could tell the difference in how the call ran after about 2 minutes of using the Shop Vac, but my call's tone board was made from hard plastic. A set of guts made from soft plastic will wear in sooner.
The average caller should be able to run a call for many hours before a reed needs to be replaced .... or, though not likely, it could develop a bubble almost immediately.