Falk, kudos to you. I know this wasn't easy. I am sorry to hear about the difficulties and challenges you have faced, but you are determined to move forward and that's what matters most.
Although it sounds like your mother isn't openly supportive at least you are not facing hostility - so your letters were already effective. I can't tell you which communication methods are best in your case, but now that she has read your letters maybe it's time for a nice talk - mixed in with other topics so she can see this from a big-picture standpoint. We often feel self-conscious for imposing on others but the fact is, it's your future and you need to make tomorrow as good as possible. I imagine you have goals that fall into both categories - things with transition, and goals not directly related to transition.
My parents are far more supportive than I expected, but even with that I have different expectations for the amount of time they will need to process and adjust to changes. The longer someone has known me, the more time they might need to reset their perception of who I am. I expect neighbors and people at work to adjust much faster, and if someone new misgenders me I quickly correct them and go on. Being misgendered by a family member is difficult to handle but just think about the future - a few months or a year goes by pretty fast when you look back on it.
I think the mind is the foundation of transition, and social transition is one of the largest accomplishments possible. There are many details to consider in each of our cases - the details that impact how we look, sound, our choice of words, body language, etc. The specific mixture of details for you will be based on your goals and what resources you have available over time, and one detail is never the entire answer. I've seen people hit a wall when one particular detail seems impossible to achieve - my recommendation is realize that's just a percentage and other things that are more achievable are probably within reach. If a boulder won't move, walk around it... sometimes you can return later and they are easier to move. Your mind is something you completely own right now and can drive the big picture - your future. I believe you are on a great path.
Kendra