Our trans brothers on this site can definitely help you figure out some effective binding methods if hiding your breasts is what you're after (please be safe when doing this! it's very important to bind in a safe way, and from what I understand, many pre-fab binders for sale are not especially good for you, more here:
https://broadly.vice.com/en_us/article/chest-binding-health-project-inside-landmark-overdue-transgender-study). Extra weight on the hips and butt can be masked with bigger / baggier clothes, to an extent.
However. I do think that this feeling "uneven"--a genius word that I think describes this feeling so perfectly as someone who is full-time, pre-HRT and scruffy almost all the time for electrolysis prep--is somewhat inevitable. And there is a sense in which delaying social transition may just make you feel more "uneven" if you go to socially transition after having physically transitioned a great deal.
Don't get me wrong, I think that if you are feeling that you need to pump the breaks in order to get ready for these big changes happening to your body, then you should do that (in consultation with your doc to go off safely). You have your whole life to become & be who you want to be.
However, if you want to stop because you you think you will be able to arrange the elements of your transition perfectly so that they culminate in one beautiful moment where you flip the switch and go from passing as a man one day to passing as a woman the next, I think you will be disappointed in the end that you let the perfect be the enemy of the good. Your goal to transition under the radar until you feel that you're "at your best" is, as you admit, a little unrealistic.
For one, practice makes perfect with things like dress sense, makeup, gestures, mannerisms, voice, etc. You can certainly practice in private as well, but there is no substitute for real life experience in some of these things--especially in boosting your confidence.
#2, Starting to socially transition also gives friends, family, partners, etc. time to get used to the idea of your transition & an opportunity to support you through the physical & mental changes you'll go through. You can imagine that revealing to a close friend or family member not only that you're trans, but that you have in fact taken all of the steps to physically transition already and your body has been slowly changing right under their noses... that might cause people to freak out a little bit, especially if they are not used to the idea of your being trans in the first place. Even supportive people might feel sad that they missed out on the opportunity to support you & experience this process with you.
#3, Hiding your transition from everyone around you until you have completed hair removal, HRT & other physical changes--sounds like you are thinking about FFS to me--would be a secret agent-level feat. Not to mention the huge amount of stress this would put on you.
Now I will admit that my tolerance for unevenness is pretty high, so that's my bias. I am thick-skinned and impatient to get my transition firing on all cylinders, so I would basically only stop for a medical reason. I am also privileged to have a job, family and friends I was pretty sure would accept my transition and support me through it. The fact that I don't pass that well right now exposes me to real risks, and I can't deny that. But I am also already seeing huge benefits from my social transition, including a lot less depression, anxiety and stress.
Whatever you decide, I wish you the best. Big hugs!