I do have a question about that. It would seem to me that it would take a missile far longer to clear a long-barreled smoothbore cannon than it would a shell that was fired. You have the tank on the move, bouncing over battle-torn fields and forests; it would seem to me that a missile would be bounced around inside the barrel of the cannon long before it was able to exit. What would be the accuracy of a missile, still under boosted power, being shaken down the barrel like a pea in a straw. When it finally exited, goodness knows what direction it would be facing, still under boost-power.
And if you're back to the situation where you have to come to a stop to fire, you're dead meat on a battlefield anyway, especially if these are wire-guided missiles and you have to remain stationary for guidance. If they're fire-and-forget, they're roman-candles. If they're laser guided, bouncing around the designator as you tool cross-country is not going to make for very good accuracy either.
Something about this just brings to mind a device that sounds good, but won't work.
Gun stabilizers have been around since WW2.
Go look at video of an M1 or Leopard 2 or Challenger in action, firing on the move. The stabilized gun sits rock steady bearing on the target while the rest of the tank bounces around.