Yes there are indeed rate and depth pots provided on the layout, i'm sure it wouldn't be much use otherwise!
With regards to the charge pump, I did consider that but decided against it for two reasons. Firstly, they have a tendency to introduce whine through the power rails, to which the ISD series is particularly sensitive. Secondly, it would require a more complicated & stable external oscillator.
In theory, regardless of the battery voltage, the regulator should always swing by the same amount though I understand that theory is not always the reality. To be honest, I only use external PSU's now so I find myself less and less concerned about battery life vs features.