"As a box player, I find the British variety rather slow to 'speak'"

As a trained pipe organ player, most big organs are slow to speak (behave yourselves you lot - get back in your cage and stand in the naughty corner!), and you learn how to 'play in anticipation'. The problem is accentuated by the acoustics of large churches, and the usual awful positioning of the player console. You sometimes get the sound from the pipes coming past the player before the congregation has heard it, and then you get the echo returning to the player, usually after the congregation has heard it! Many untrained players cause the 'hymn getting terminally slower' syndrome, because they try to listen to the singers - this is a big no-no!

There is only one technique that works - play the piece 'as if you are deaf' - and keep strict time. This means however in ensemble playing, that often some sort of musical director/condusctor is need if changes of pace to keep up with a soloist who 'bends the tempo' are needed.

The same trick applies to squeezeboxes/harmoniums that are slow to speak. Piano accordions are really just 'chest pipe organs'.