I had a very similar UC. Labor progressed well, transition was about 20-30 minutes and then ctx spaced out to one every 5 min for about 30 minutes or an hour . . . then picked up again, but no pushing urge. All of these contractions were incredibly painful and intense, like transition contractions. At 19 hours (after 6 hours of being stuck at 9cm+ in extreme pain), we transferred. MD was able to push the lip of cervix out of the way, I was told to push, and dd was born 25 minutes later. Total 21 hour labor.
It took me a very long time to process the birth and my feelings about UC. It has been an incredibly learning experience and journey. First of all, I don't consider my UC to be a failure. Maybe I needed to transfer, maybe I didn't. I think I did, because I waited so long and I was exhausted and worn and felt that the baby should have arrived by then. In a way, it's a UC success. UC is not about staying home at all costs or under all circumstances. You have to be able to transfer if you need help at some point. There is no shame in that. There's no manual for birth (okay, there are a zillion, but there's no manual for how you'll birth for a particular birth). Birth is unpredictable and different for every woman for every baby. Most of the time, everything goes off without a hitch. Sometimes, something unusual happens, and it's beneficial to have assistance. That's what it's there for.
You waited, you did beautifully, you took care of yourself. You transferred when something unusual happened that you did not feel you could handle yourselves. That's success, not failure. You gave your baby a healthy birth. You gave your baby a healthy labor and a safe birth. You only sought medical care when you needed it. I think you and your dh did a wonderful job.
Take plenty of time to absorb what happened and process the birth. Take as much time as you need. It was 7 or so months until I wrote out my birthstory. I needed that much time to work through it before I could bring myself to write it down. I felt a lot of betrayal and disappointment. I feel good about the birth now - I accept the bad and celebrate the good. I use it to help me plan for the next birth. And I don't feel like a failure, for myself or for my baby. I did what I needed to do (maybe not what the next woman would need, but what I needed) to give her the healthiest possible birth. I'm glad we went the UC route and had the long, unassisted labor at home. I'm glad we made the decision to transfer. I'm glad we had a good backup plan in hand for just such a situation. For a time I second-guessed the decision to transfer and even felt regret, thinking, "If I'd just . . ." But the thing is, I don't know what would have happened if I'd done something else, and neither does anyone else. You can speculate to help you learn from the experience, but I think at the end of the day, finding a definitive answer to a "What if I'd just stayed home?" question isn't really out there. It's one of the mysteries of the universe that will never be revealed. And so you have the birth you had, and you did beautifully, and you have so much to learn from.
Feel free to PM me if you want to talk more. I really do understand. Be gentle with yourself and take as much time as you need to process.