Wonderful! Thanks so much for all the wise and considered responses.
I'm particularly fascinated by the idea of playing an octave 1-3. I'm not sitting at my piano right now, but next time I am, you can be sure I'll be giving that a try...
As for the, let's say, more normal suggestion of mixing 1-5 and 1-4: I've never really understand what that's helpful for. It always seemed to me to be much simpler and more reliable just to lock the hand in position and play all the octaves 1-5 but thinking about Becky's post, this makes a lot of sense in this context. I'm always looking for ways to avoid using the pedal!
That said, perhaps my unwillingness to use the pedal comes from my all or nothing approach. I've never really thought of the pedal as being something to be pressed subtly. Thanks quantum for your nicely worded suggestion of "touches of pedal".