Just a quick post to close this down, for anyone following and searching for info.
I am so pleased that we now have a pretty great little sleeper, especially compared to how it was. She falls asleep within 10 minutes, usually, of going to bed, often quicker. Also re settles very well with a quick few words whispered through the door.
Mostly, I believe this is down to the gradual withdrawal process; it was long, and hard, but so worth it.
With regard to the over tiredness, while I think she was ready to move to one nap a day, I don't think she was ready to have that around midday, as she is clearly tired about 10am.
I have found that if I let her sleep between 10-10.30 for as long as she likes, we get some great 2-3 hour naps, much better than the 1.5 max I would mostly get if I waited until 12. And then I just move her bedtime earlier, depending on how early she goes down/wakes up from that one snooze a day. Catnaps just never seemed to work for us strangely.
I have found she throws less tantrums, and is not as easily frustrated now I have all this under control. I thought these were just part of her personality - it's amazing what some decent sleep can fix. For now anyway!!
