I understand wanting to think and process and work through everything. I think that too is part of grieving. ((hugs))
I transferred after 19+hrs UC labor due to my own exhaustion and concern that something was "not right" with how I felt and no appearance of baby. When I contemplate my next birth, I go back and forth all the time, I want to UC, but I'm not sure I'm really ready to do that next time.
I've spent countless hours working this over in my mind. For me, I am going to try to have a homebirth with a very hands-off midwife. Because my last UC didn't go as smoothly as I expected (and I'm not comparing mine to yours at all, just that it was harder than I thought UC would be and I did in the end benefit from someone being able to tell me what was going on), next time I want to do it with someone there. Someone who will sit in the corner or another room and just let me and dh do our thing, and we can ask for help if we need it.
I'm leaving room in my heart for UC for baby #3 or 4, too. I am still powerfully attracted to UC, but I know that for me it wouldn't be beneficial to labor while worrying about the what ifs. I think it has a lot to do with a deep, deep comfort level. I think a 2nd birth would be easier, and therefore UC more likely. But deep inside I'm not ready to UC again yet. I need someone there to calm that fear, just by being present (and practically invisible). I know that I will labor better with a "backup"/"resource" within easy reach.
But all of that is just completely personal to me. It has taken me many months to get to this point, where I feel like I have an idea what I want to do and feel reasonably comfortable with it. I think you're doing the right thing in starting to process and think . . . just realize that it will probably be a long time before you find an answer you feel comfortable with.
We had a discussion here recently about "freebirth" verus "UC." I like the reasons that were given for "freebirth" as a descriptor, because it means we're free to labor and birth in whatever way is most right and comfortable for us. I know if you keep searching you'll find the answer to the question of how you want to give birth next time.
((hugs)) and love to you and your family.