It's perfectly easy to get an instantaneous 70 W out of a transformer rated at 30-50 VA. You just draw as much current as the load needs and let the transformer do its thing.
And to expand on that a little bit.
To achieve that, they go down on the number of turns on the primary, which means higher current through it, and thereby forcing the secondary to deliver more (if the wire thickness allows it to), which again means that the transformer automatically gets better self-regulating properties also. But, the transformer core needs to be able to handle the increased current, so they use High Flux Density cores for this.
A ''stiff'' (good self regulation) transformer, typical 10 percent or better is easily recognized by a low DC resistance primary with solid enameled wire, compared to others of the same size. And, if someone noticed the voltage drop on Miles' new transformer, he has just got one of the stiff ones in his '888.
I'm actually tempted to write Miles a PM and ask if he can fix a transformer for me.