TLDR = 90% in terms of dysphoria and the crushing feeling of being a guy, but like 33% in terms of actually living life as a girl and swimming through the sea of transition.
Long answer incoming:
The key words in the question are dysphoria, managed, and estrogen alone.
My whole issue in my life, even as a kid, was this itch to be female. I don't know why and never will know why. I do know the when (age 4) and I knew the how of how to fix it (E), again, even as a kid. My mom's supplement pills for women were stolen a number of times because I felt that that would contain hormones to make everything right...I was like 10 years old then! So I believe that dysphoria has different definitions/descriptions for different folks. My dysphoria is pretty damn simple: Incongruent mind/body. My mind wanted to be 1) expressive with nail polish, makeup, jewelry, feminine attire 2) to be able to be free in my thoughts and opinions of the world without just being labeled a gay male 3) to be comfortable in society with the physical things I needed to have: hairless body, small frame, long hair, boobies... but my body was sooo masculine and I looked/felt like a weirdo whenever I dressed. So it was this horrible, horrible feeling in my head of these contradictory polarities butting heads --> serenity of expressing my femininity but the reality of being a dude and it all be wrong. THIS IS DYSHPORIA!!! That's how I describe it anyway. So having E in me has changed me not only mentally but physically and it is through this change that that feeling has been 90% managed by E alone... the other 10% is my plumbing hehe. Like, that's pretty much the only time I feel that incongruence still... besides being pre-op my dysphoria has been nullified, so that's the good news!
The 33% number I came up with in terms of transition, though, is mainly due to the fact that I didn't realize how much of living as a girl full-time (from living as a guy) is a mental process. That is NOT to say that "passing is mostly attitude!" That's a bunch of crap in my opinion. I'm not really talking about passing though, just what is needed to transition well, mentally. What I mean is that self acceptance, will power, courage, dedication, patience... all of those things I don't believe E alone manages, but they need to be tackled and mastered during transition. That's what I didn't see coming early in my transition...the mental hurdles that lay ahead which had nothing to do with my physical body.