Hi skywalker, I'm using a LM3576 switching regulator down from 9 volts, as for the peeks I have a 4700uF cap before the regulator, and a 3300uF cap as part of the regulator circuit (mentioned in the design notes). In practice I haven't seen it draw more than an amp (using dial up, or GRPS).
As for turning it on / off, I'm using a attiny15 microcontroller to monitor the 2.7volt line and control the on/off pins of the regulator, and the on/off toggle pin of the GR47. I did this as the power cycling procedure needs to be controlled better than the RC network they suggest. If you have another micro on board I would suggest using spare pins of that.