(This isn't the most positive of stories, but as you say, I got a healthy baby and I'm happy with it now, though was a bit upset immediately afterwards.)
I had DD2 7 weeks ago in similar circumstances. I was 39+3 though, so further along. I had also been hoping for a homebirth as I had one with DD1, but my waters broke and very little happened. After 24 hours they asked me to come in to be induced. It actually took ages to be hooked up to the drip as the hospital got incredibly busy.
Things got going pretty quickly once the midwife started the drip. I was at 3cm when they examined me before putting the drip in, and went from that to giving birth in 2 and a half hours.
They start it at a low level then crank it up every half hour. In hindsight I could have communicated more with the midwife as she was waiting for 4 contractions in 10 minutes before she would stop upping the level of syntocin, but I never got to that point. I had a feeling things were happening, and felt like I could be in transition (felt weak, a bit sick, and like I couldn't cope with it), but because I'd been quiet the midwife didn't have a clue how far along I was and kept increasing the drip. As a result second stage was incredibly quick (10mins), I felt like I had very little control over what was happening to me, and I got a third degree tear.
Sorry, probably not the sort of story you want, but I'll post as you asked for experiences. At 7 weeks post partum I've healed well and all is going well with DD2 :)